The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
GEOMETRY
Thursday, August 17, 2023 — 12:30 to 3:30 p.m., only
MODEL RESPONSE SET
Table of Contents
Question 25 ....................................... 2
Question 26 ..................................... 10
Question 27 ..................................... 15
Question 28 ..................................... 21
Question 29 ..................................... 29
Question 30 ..................................... 35
Question 31 ..................................... 42
Question 32 ..................................... 49
Question 33 ..................................... 59
Question 34 ..................................... 69
Question 35 ..................................... 81
Question 25
Geometry – Aug. ’23 [2]
Geometry – Aug. ’23 [12]
Part II
Answer all 7 questions in this part. Each correct answer will receive 2 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided for each question to determine your answer.
Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct
numerical answer with no work shown will receive only 1 credit. All answers should be
written in pen, except for graphs and drawings, which should be done in pencil. [
14]
25 On the set of axes below, congruent quadrilaterals ROCK and R9O9C9K9 are graphed.
y
x
R9
K9
O9
C9
K
C
O
R
Describe a sequence of transformations that would map quadrilateral ROCK onto
quadrilateral R9O9C9K9.
Score 2: The student gave a complete and correct response.
Question 25
Geometry – Aug. ’23 [3]
Geometry – Aug. ’23 [12]
Part II
Answer all 7 questions in this part. Each correct answer will receive 2 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided for each question to determine your answer.
Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct
numerical answer with no work shown will receive only 1 credit. All answers should be
written in pen, except for graphs and drawings, which should be done in pencil. [
14]
25 On the set of axes below, congruent quadrilaterals ROCK and R9O9C9K9 are graphed.
y
x
R9
K9
O9
C9
K
C
O
R
Describe a sequence of transformations that would map quadrilateral ROCK onto
quadrilateral R9O9C9K9.
Score 2: The student gave a complete and correct response.
Question 25
Geometry – Aug. ’23 [4]
Geometry – Aug. ’23 [12]
Part II
Answer all 7 questions in this part. Each correct answer will receive 2 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided for each question to determine your answer.
Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct
numerical answer with no work shown will receive only 1 credit. All answers should be
written in pen, except for graphs and drawings, which should be done in pencil. [
14]
25 On the set of axes below, congruent quadrilaterals ROCK and R9O9C9K9 are graphed.
y
x
R9
K9
O9
C9
K
C
O
R
Describe a sequence of transformations that would map quadrilateral ROCK onto
quadrilateral R9O9C9K9.
Score 2: The student gave a complete and correct response.
Question 25
Geometry – Aug. ’23 [5]
Geometry – Aug. ’23 [12]
Part II
Answer all 7 questions in this part. Each correct answer will receive 2 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided for each question to determine your answer.
Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct
numerical answer with no work shown will receive only 1 credit. All answers should be
written in pen, except for graphs and drawings, which should be done in pencil. [
14]
25 On the set of axes below, congruent quadrilaterals ROCK and R9O9C9K9 are graphed.
y
x
R9
K9
O9
C9
K
C
O
R
Describe a sequence of transformations that would map quadrilateral ROCK onto
quadrilateral R9O9C9K9.
Score 2: The student gave a complete and correct response.
Question 25
Geometry – Aug. ’23 [6]
Geometry – Aug. ’23 [12]
Part II
Answer all 7 questions in this part. Each correct answer will receive 2 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided for each question to determine your answer.
Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct
numerical answer with no work shown will receive only 1 credit. All answers should be
written in pen, except for graphs and drawings, which should be done in pencil. [
14]
25 On the set of axes below, congruent quadrilaterals ROCK and R9O9C9K9 are graphed.
y
x
R9
K9
O9
C9
K
C
O
R
Describe a sequence of transformations that would map quadrilateral ROCK onto
quadrilateral R9O9C9K9.
Score 1: The student stated an incorrect coordinate as the center of rotation.
Question 25
Geometry – Aug. ’23 [7]
Geometry – Aug. ’23 [12]
Part II
Answer all 7 questions in this part. Each correct answer will receive 2 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided for each question to determine your answer.
Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct
numerical answer with no work shown will receive only 1 credit. All answers should be
written in pen, except for graphs and drawings, which should be done in pencil. [
14]
25 On the set of axes below, congruent quadrilaterals ROCK and R9O9C9K9 are graphed.
y
x
R9
K9
O9
C9
K
C
O
R
Describe a sequence of transformations that would map quadrilateral ROCK onto
quadrilateral R9O9C9K9.
Score 1: The student determined the sequence of transformations correctly, but stated the
translations incorrectly as T
1,0
and T
0,22
, rather than T
0,1
and T
22,0
.
Question 25
Geometry – Aug. ’23 [8]
Geometry – Aug. ’23 [12]
Part II
Answer all 7 questions in this part. Each correct answer will receive 2 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided for each question to determine your answer.
Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct
numerical answer with no work shown will receive only 1 credit. All answers should be
written in pen, except for graphs and drawings, which should be done in pencil. [
14]
25 On the set of axes below, congruent quadrilaterals ROCK and R9O9C9K9 are graphed.
y
x
R9
K9
O9
C9
K
C
O
R
Describe a sequence of transformations that would map quadrilateral ROCK onto
quadrilateral R9O9C9K9.
Score 0: The student did not show enough correct relevant course-level work to receive any credit.
Question 25
Geometry – Aug. ’23 [9]
Geometry – Aug. ’23 [12]
Part II
Answer all 7 questions in this part. Each correct answer will receive 2 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided for each question to determine your answer.
Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct
numerical answer with no work shown will receive only 1 credit. All answers should be
written in pen, except for graphs and drawings, which should be done in pencil. [
14]
25 On the set of axes below, congruent quadrilaterals ROCK and R9O9C9K9 are graphed.
y
x
R9
K9
O9
C9
K
C
O
R
Describe a sequence of transformations that would map quadrilateral ROCK onto
quadrilateral R9O9C9K9.
Score 0: The student did not show enough correct relevant work to receive any credit.
Question 26
Geometry – Aug. ’23 [10]
Geometry – Aug. ’23 [13] [OVER]
26 In triangle CEM, CE 5 3x 1 10, ME 5 5x 2 14, and CM 5 2x 2 6.
Determine and state the value of x that would make nCEM an isosceles triangle with
the vertex angle at E.
Score 2: The student gave a complete and correct response.
Question 26
Geometry – Aug. ’23 [11]
Geometry – Aug. ’23 [13] [OVER]
26 In triangle CEM, CE 5 3x 1 10, ME 5 5x 2 14, and CM 5 2x 2 6.
Determine and state the value of x that would make nCEM an isosceles triangle with
the vertex angle at E.
Score 2: The student gave a complete and correct response.
Question 26
Geometry – Aug. ’23 [12]
Geometry – Aug. ’23 [13] [OVER]
26 In triangle CEM, CE 5 3x 1 10, ME 5 5x 2 14, and CM 5 2x 2 6.
Determine and state the value of x that would make nCEM an isosceles triangle with
the vertex angle at E.
Score 1: The student wrote an incorrect equation, but found an appropriate value of x.
Question 26
Geometry – Aug. ’23 [13]
Geometry – Aug. ’23 [13] [OVER]
26 In triangle CEM, CE 5 3x 1 10, ME 5 5x 2 14, and CM 5 2x 2 6.
Determine and state the value of x that would make nCEM an isosceles triangle with
the vertex angle at E.
Score 0: The student did not show enough correct relevant course-level work to receive any credit.
Question 26
Geometry – Aug. ’23 [14]
Geometry – Aug. ’23 [13] [OVER]
26 In triangle CEM, CE 5 3x 1 10, ME 5 5x 2 14, and CM 5 2x 2 6.
Determine and state the value of x that would make nCEM an isosceles triangle with
the vertex angle at E.
Score 0: The student gave a completely incorrect response.
Question 27
Geometry – Aug. ’23 [15]
Geometry – Aug. ’23 [14]
27 A flagpole casts a shadow on the ground 91 feet long, with a 53° angle of elevation from the end
of the shadow to the top of the flagpole.
Determine and state, to the nearest tenth of a foot, the height of the flagpole.
Score 2: The student gave a complete and correct response.
Question 27
Geometry – Aug. ’23 [16]
Geometry – Aug. ’23 [14]
27 A flagpole casts a shadow on the ground 91 feet long, with a 53° angle of elevation from the end
of the shadow to the top of the flagpole.
Determine and state, to the nearest tenth of a foot, the height of the flagpole.
Score 2: The student gave a complete and correct response.
Question 27
Geometry – Aug. ’23 [17]
Geometry – Aug. ’23 [14]
27 A flagpole casts a shadow on the ground 91 feet long, with a 53° angle of elevation from the end
of the shadow to the top of the flagpole.
Determine and state, to the nearest tenth of a foot, the height of the flagpole.
Score 1: The student made a rounding error.
Question 27
Geometry – Aug. ’23 [18]
Geometry – Aug. ’23 [14]
27 A flagpole casts a shadow on the ground 91 feet long, with a 53° angle of elevation from the end
of the shadow to the top of the flagpole.
Determine and state, to the nearest tenth of a foot, the height of the flagpole.
Score 1: The student wrote a correct relevant trigonometric equation, but no further correct work
was shown.
Question 27
Geometry – Aug. ’23 [19]
Geometry – Aug. ’23 [14]
27 A flagpole casts a shadow on the ground 91 feet long, with a 53° angle of elevation from the end
of the shadow to the top of the flagpole.
Determine and state, to the nearest tenth of a foot, the height of the flagpole.
Score 1: The student used an incorrect trigonometric equation, but found an appropriate answer.
Question 27
Geometry – Aug. ’23 [20]
Geometry – Aug. ’23 [14]
27 A flagpole casts a shadow on the ground 91 feet long, with a 53° angle of elevation from the end
of the shadow to the top of the flagpole.
Determine and state, to the nearest tenth of a foot, the height of the flagpole.
Score 0: The student gave a completely incorrect response.
Question 28
Geometry – Aug. ’23 [21]
Geometry – Aug. ’23 [15] [OVER]
28 A man is spray-painting the tops of 10 patio tables. Five tables have round tops, with diameters
of 4 feet, and five tables have rectangular tops, with dimensions of 4 feet by 6 feet. A can of spray
paint covers 25 square feet. How many cans of spray paint must be purchased to paint all of the
tabletops?
Score 2: The student gave a complete and correct response.
Question 28
Geometry – Aug. ’23 [22]
Geometry – Aug. ’23 [15] [OVER]
28 A man is spray-painting the tops of 10 patio tables. Five tables have round tops, with diameters
of 4 feet, and five tables have rectangular tops, with dimensions of 4 feet by 6 feet. A can of spray
paint covers 25 square feet. How many cans of spray paint must be purchased to paint all of the
tabletops?
Score 2: The student gave a complete and correct response.
Question 28
Geometry – Aug. ’23 [23]
Geometry – Aug. ’23 [15] [OVER]
28 A man is spray-painting the tops of 10 patio tables. Five tables have round tops, with diameters
of 4 feet, and five tables have rectangular tops, with dimensions of 4 feet by 6 feet. A can of spray
paint covers 25 square feet. How many cans of spray paint must be purchased to paint all of the
tabletops?
Score 2: The student gave a complete and correct response.
Question 28
Geometry – Aug. ’23 [24]
Geometry – Aug. ’23 [15] [OVER]
28 A man is spray-painting the tops of 10 patio tables. Five tables have round tops, with diameters
of 4 feet, and five tables have rectangular tops, with dimensions of 4 feet by 6 feet. A can of spray
paint covers 25 square feet. How many cans of spray paint must be purchased to paint all of the
tabletops?
Score 1: The student made a computational error.
Question 28
Geometry – Aug. ’23 [25]
Geometry – Aug. ’23 [15] [OVER]
28 A man is spray-painting the tops of 10 patio tables. Five tables have round tops, with diameters
of 4 feet, and five tables have rectangular tops, with dimensions of 4 feet by 6 feet. A can of spray
paint covers 25 square feet. How many cans of spray paint must be purchased to paint all of the
tabletops?
Score 1: The student determined the total area of the ten tables, but no further correct work was
shown.
Question 28
Geometry – Aug. ’23 [26]
Geometry – Aug. ’23 [15] [OVER]
28 A man is spray-painting the tops of 10 patio tables. Five tables have round tops, with diameters
of 4 feet, and five tables have rectangular tops, with dimensions of 4 feet by 6 feet. A can of spray
paint covers 25 square feet. How many cans of spray paint must be purchased to paint all of the
tabletops?
Score 1: The student made a transposition error when determining the total area of the ten tables.
Question 28
Geometry – Aug. ’23 [27]
Geometry – Aug. ’23 [15] [OVER]
28 A man is spray-painting the tops of 10 patio tables. Five tables have round tops, with diameters
of 4 feet, and five tables have rectangular tops, with dimensions of 4 feet by 6 feet. A can of spray
paint covers 25 square feet. How many cans of spray paint must be purchased to paint all of the
tabletops?
Score 1: The student made a computational error in determining the area of the ve rectangular
tables.
Question 28
Geometry – Aug. ’23 [28]
Geometry – Aug. ’23 [15] [OVER]
28 A man is spray-painting the tops of 10 patio tables. Five tables have round tops, with diameters
of 4 feet, and five tables have rectangular tops, with dimensions of 4 feet by 6 feet. A can of spray
paint covers 25 square feet. How many cans of spray paint must be purchased to paint all of the
tabletops?
Score 0: The student used an incorrect radius when determining the area of the ve round tables.
The student made a computational error when determining the number of cans.
Question 29
Geometry – Aug. ’23 [29]
Geometry – Aug. ’23 [16]
29 Using a compass and straightedge, construct a midsegment of nAHL below.
[Leave all construction marks.]
A
H
L
Score 2: The student gave a complete and correct response.
Question 29
Geometry – Aug. ’23 [30]
Geometry – Aug. ’23 [16]
29 Using a compass and straightedge, construct a midsegment of nAHL below.
[Leave all construction marks.]
A
H
L
Score 1: The student constructed the perpendicular bisectors of the sides of nAHL, but did not
draw the midsegment.
Question 29
Geometry – Aug. ’23 [31]
Geometry – Aug. ’23 [16]
29 Using a compass and straightedge, construct a midsegment of nAHL below.
[Leave all construction marks.]
A
H
L
Score 0: The student did not show enough correct work to receive any credit.
Question 29
Geometry – Aug. ’23 [32]
Geometry – Aug. ’23 [16]
29 Using a compass and straightedge, construct a midsegment of nAHL below.
[Leave all construction marks.]
A
H
L
Score 0: The student did not show enough correct work to receive any credit.
Question 29
Geometry – Aug. ’23 [33]
Geometry – Aug. ’23 [16]
29 Using a compass and straightedge, construct a midsegment of nAHL below.
[Leave all construction marks.]
A
H
L
Score 0: The student gave a completely incorrect response.
Question 29
Geometry – Aug. ’23 [34]
Geometry – Aug. ’23 [16]
29 Using a compass and straightedge, construct a midsegment of nAHL below.
[Leave all construction marks.]
A
H
L
Score 0: The student gave a completely incorrect response.
Question 30
Geometry – Aug. ’23 [35]
Geometry – Aug. ’23 [17] [OVER]
30 Right triangle STR is shown below, with m/T 5 90°. Altitude
TQ
is drawn to
SQR
, and TQ 5 8.
T
S R
Q
8
If the ratio SQ:QR is 1:4, determine and state the length of
SR
.
Score 2: The student gave a complete and correct response.
Question 30
Geometry – Aug. ’23 [36]
Geometry – Aug. ’23 [17] [OVER]
30 Right triangle STR is shown below, with m/T 5 90°. Altitude
TQ
is drawn to
SQR
, and TQ 5 8.
T
S R
Q
8
If the ratio SQ:QR is 1:4, determine and state the length of
SR
.
Score 2: The student gave a complete and correct response.
Question 30
Geometry – Aug. ’23 [37]
Geometry – Aug. ’23 [17] [OVER]
30 Right triangle STR is shown below, with m/T 5 90°. Altitude
TQ
is drawn to
SQR
, and TQ 5 8.
T
S R
Q
8
If the ratio SQ:QR is 1:4, determine and state the length of
SR
.
Score 1: The student made a computational error.
Question 30
Geometry – Aug. ’23 [38]
Geometry – Aug. ’23 [17] [OVER]
30 Right triangle STR is shown below, with m/T 5 90°. Altitude
TQ
is drawn to
SQR
, and TQ 5 8.
T
S R
Q
8
If the ratio SQ:QR is 1:4, determine and state the length of
SR
.
Score 1: The student made a computational error.
Question 30
Geometry – Aug. ’23 [39]
Geometry – Aug. ’23 [17] [OVER]
30 Right triangle STR is shown below, with m/T 5 90°. Altitude
TQ
is drawn to
SQR
, and TQ 5 8.
T
S R
Q
8
If the ratio SQ:QR is 1:4, determine and state the length of
SR
.
Score 1: The student correctly determined the length of
SQ
, but no further correct work was
shown.
Question 30
Geometry – Aug. ’23 [40]
Geometry – Aug. ’23 [17] [OVER]
30 Right triangle STR is shown below, with m/T 5 90°. Altitude
TQ
is drawn to
SQR
, and TQ 5 8.
T
S R
Q
8
If the ratio SQ:QR is 1:4, determine and state the length of
SR
.
Score 0: The student wrote an incorrect proportion and solved the proportion incorrectly, thus
obtaining a correct answer by an incorrect procedure.
Question 30
Geometry – Aug. ’23 [41]
Geometry – Aug. ’23 [17] [OVER]
30 Right triangle STR is shown below, with m/T 5 90°. Altitude
TQ
is drawn to
SQR
, and TQ 5 8.
T
S R
Q
8
If the ratio SQ:QR is 1:4, determine and state the length of
SR
.
Score 0: The student gave a completely incorrect response.
Question 31
Geometry – Aug. ’23 [42]
Geometry – Aug. ’23 [18]
31 Line AB is dilated by a scale factor of 2 centered at point A.
A
B
Evan thinks that the dilation of
AB
will result in a line parallel to
AB
, not passing through points
A or B.
Nathan thinks that the dilation of
AB
will result in the same line,
AB
.
Who is correct?
Explain why.
Score 2: The student wrote a complete and correct response.
Question 31
Geometry – Aug. ’23 [43]
Geometry – Aug. ’23 [18]
31 Line AB is dilated by a scale factor of 2 centered at point A.
A
B
Evan thinks that the dilation of
AB
will result in a line parallel to
AB
, not passing through points
A or B.
Nathan thinks that the dilation of
AB
will result in the same line,
AB
.
Who is correct?
Explain why.
Score 2: The student wrote a complete and correct response.
Question 31
Geometry – Aug. ’23 [44]
Geometry – Aug. ’23 [18]
31 Line AB is dilated by a scale factor of 2 centered at point A.
A
B
Evan thinks that the dilation of
AB
will result in a line parallel to
AB
, not passing through points
A or B.
Nathan thinks that the dilation of
AB
will result in the same line,
AB
.
Who is correct?
Explain why.
Score 2: The student wrote a complete and correct response.
Question 31
Geometry – Aug. ’23 [45]
Geometry – Aug. ’23 [18]
31 Line AB is dilated by a scale factor of 2 centered at point A.
A
B
Evan thinks that the dilation of
AB
will result in a line parallel to
AB
, not passing through points
A or B.
Nathan thinks that the dilation of
AB
will result in the same line,
AB
.
Who is correct?
Explain why.
Score 1: The student wrote a partially correct explanation.
Question 31
Geometry – Aug. ’23 [46]
Geometry – Aug. ’23 [18]
31 Line AB is dilated by a scale factor of 2 centered at point A.
A
B
Evan thinks that the dilation of
AB
will result in a line parallel to
AB
, not passing through points
A or B.
Nathan thinks that the dilation of
AB
will result in the same line,
AB
.
Who is correct?
Explain why.
Score 1: The student wrote a partially correct explanation.
Question 31
Geometry – Aug. ’23 [47]
Geometry – Aug. ’23 [18]
31 Line AB is dilated by a scale factor of 2 centered at point A.
A
B
Evan thinks that the dilation of
AB
will result in a line parallel to
AB
, not passing through points
A or B.
Nathan thinks that the dilation of
AB
will result in the same line,
AB
.
Who is correct?
Explain why.
Score 0: The student wrote an incorrect explanation.
Question 31
Geometry – Aug. ’23 [48]
Geometry – Aug. ’23 [18]
31 Line AB is dilated by a scale factor of 2 centered at point A.
A
B
Evan thinks that the dilation of
AB
will result in a line parallel to
AB
, not passing through points
A or B.
Nathan thinks that the dilation of
AB
will result in the same line,
AB
.
Who is correct?
Explain why.
Score 0: The student wrote an incorrect explanation.
Question 32
Geometry – Aug. ’23 [49]
Geometry – Aug. ’23 [19] [OVER]
Part III
Answer all 3 questions in this part. Each correct answer will receive 4 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided for each question to determine your answer.
Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct
numerical answer with no work shown will receive only 1 credit. All answers should be
written in pen, except for graphs and drawings, which should be done in pencil. [
12]
32 Josh is making a square-based fire pit out of concrete for his backyard, as modeled by the right
prism below. He plans to make the outside walls of the fire pit 3.5 feet on each side with a height
of 1.5 feet. The concrete walls of the re pit are going to be 9 inches thick.
9 in
3.5 ft
1.5 ft
If a bag of concrete mix will ll 0.6 ft
3
, determine and state the minimum number of bags needed
to build the re pit.
Score 4: The student gave a complete and correct response.
Question 32
Geometry – Aug. ’23 [50]
Geometry – Aug. ’23 [19] [OVER]
Part III
Answer all 3 questions in this part. Each correct answer will receive 4 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided for each question to determine your answer.
Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct
numerical answer with no work shown will receive only 1 credit. All answers should be
written in pen, except for graphs and drawings, which should be done in pencil. [
12]
32 Josh is making a square-based fire pit out of concrete for his backyard, as modeled by the right
prism below. He plans to make the outside walls of the fire pit 3.5 feet on each side with a height
of 1.5 feet. The concrete walls of the re pit are going to be 9 inches thick.
9 in
3.5 ft
1.5 ft
If a bag of concrete mix will ll 0.6 ft
3
, determine and state the minimum number of bags needed
to build the re pit.
Score 4: The student gave a complete and correct response.
Question 32
Geometry – Aug. ’23 [51]
Geometry – Aug. ’23 [19] [OVER]
Part III
Answer all 3 questions in this part. Each correct answer will receive 4 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided for each question to determine your answer.
Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct
numerical answer with no work shown will receive only 1 credit. All answers should be
written in pen, except for graphs and drawings, which should be done in pencil. [
12]
32 Josh is making a square-based fire pit out of concrete for his backyard, as modeled by the right
prism below. He plans to make the outside walls of the fire pit 3.5 feet on each side with a height
of 1.5 feet. The concrete walls of the re pit are going to be 9 inches thick.
9 in
3.5 ft
1.5 ft
If a bag of concrete mix will ll 0.6 ft
3
, determine and state the minimum number of bags needed
to build the re pit.
Score 4: The student gave a complete and correct response.
Question 32
Geometry – Aug. ’23 [52]
Geometry – Aug. ’23 [19] [OVER]
Part III
Answer all 3 questions in this part. Each correct answer will receive 4 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided for each question to determine your answer.
Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct
numerical answer with no work shown will receive only 1 credit. All answers should be
written in pen, except for graphs and drawings, which should be done in pencil. [
12]
32 Josh is making a square-based fire pit out of concrete for his backyard, as modeled by the right
prism below. He plans to make the outside walls of the fire pit 3.5 feet on each side with a height
of 1.5 feet. The concrete walls of the re pit are going to be 9 inches thick.
9 in
3.5 ft
1.5 ft
If a bag of concrete mix will ll 0.6 ft
3
, determine and state the minimum number of bags needed
to build the re pit.
Score 3: The student made a computational error in determining the volume of the inner region
of the re pit.
Question 32
Geometry – Aug. ’23 [53]
Geometry – Aug. ’23 [19] [OVER]
Part III
Answer all 3 questions in this part. Each correct answer will receive 4 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided for each question to determine your answer.
Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct
numerical answer with no work shown will receive only 1 credit. All answers should be
written in pen, except for graphs and drawings, which should be done in pencil. [
12]
32 Josh is making a square-based fire pit out of concrete for his backyard, as modeled by the right
prism below. He plans to make the outside walls of the fire pit 3.5 feet on each side with a height
of 1.5 feet. The concrete walls of the re pit are going to be 9 inches thick.
9 in
3.5 ft
1.5 ft
If a bag of concrete mix will ll 0.6 ft
3
, determine and state the minimum number of bags needed
to build the re pit.
Score 3: The student used an incorrect height when determining the volume of the inner region
of the re pit.
Question 32
Geometry – Aug. ’23 [54]
Geometry – Aug. ’23 [19] [OVER]
Part III
Answer all 3 questions in this part. Each correct answer will receive 4 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided for each question to determine your answer.
Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct
numerical answer with no work shown will receive only 1 credit. All answers should be
written in pen, except for graphs and drawings, which should be done in pencil. [
12]
32 Josh is making a square-based fire pit out of concrete for his backyard, as modeled by the right
prism below. He plans to make the outside walls of the fire pit 3.5 feet on each side with a height
of 1.5 feet. The concrete walls of the re pit are going to be 9 inches thick.
9 in
3.5 ft
1.5 ft
If a bag of concrete mix will ll 0.6 ft
3
, determine and state the minimum number of bags needed
to build the re pit.
Score 3: The student did not convert the volume of concrete to cubic feet.
Question 32
Geometry – Aug. ’23 [55]
Geometry – Aug. ’23 [19] [OVER]
Part III
Answer all 3 questions in this part. Each correct answer will receive 4 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided for each question to determine your answer.
Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct
numerical answer with no work shown will receive only 1 credit. All answers should be
written in pen, except for graphs and drawings, which should be done in pencil. [
12]
32 Josh is making a square-based fire pit out of concrete for his backyard, as modeled by the right
prism below. He plans to make the outside walls of the fire pit 3.5 feet on each side with a height
of 1.5 feet. The concrete walls of the re pit are going to be 9 inches thick.
9 in
3.5 ft
1.5 ft
If a bag of concrete mix will ll 0.6 ft
3
, determine and state the minimum number of bags needed
to build the re pit.
Score 2: The student made a conceptual error when determining the volume of both the outside
rectangular prism and the inner region of the re pit.
Question 32
Geometry – Aug. ’23 [56]
Geometry – Aug. ’23 [19] [OVER]
Part III
Answer all 3 questions in this part. Each correct answer will receive 4 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided for each question to determine your answer.
Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct
numerical answer with no work shown will receive only 1 credit. All answers should be
written in pen, except for graphs and drawings, which should be done in pencil. [
12]
32 Josh is making a square-based fire pit out of concrete for his backyard, as modeled by the right
prism below. He plans to make the outside walls of the fire pit 3.5 feet on each side with a height
of 1.5 feet. The concrete walls of the re pit are going to be 9 inches thick.
9 in
3.5 ft
1.5 ft
If a bag of concrete mix will ll 0.6 ft
3
, determine and state the minimum number of bags needed
to build the re pit.
Score 1: The student made a conceptual error in determining the volume of both the outside
rectangular prism and inner region of the re pit. The student made a rounding error in
determining the number of bags of concrete.
Question 32
Geometry – Aug. ’23 [57]
Geometry – Aug. ’23 [19] [OVER]
Part III
Answer all 3 questions in this part. Each correct answer will receive 4 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided for each question to determine your answer.
Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct
numerical answer with no work shown will receive only 1 credit. All answers should be
written in pen, except for graphs and drawings, which should be done in pencil. [
12]
32 Josh is making a square-based fire pit out of concrete for his backyard, as modeled by the right
prism below. He plans to make the outside walls of the fire pit 3.5 feet on each side with a height
of 1.5 feet. The concrete walls of the re pit are going to be 9 inches thick.
9 in
3.5 ft
1.5 ft
If a bag of concrete mix will ll 0.6 ft
3
, determine and state the minimum number of bags needed
to build the re pit.
Score 1: The student determined the volume of the outside rectangular prism, but no further
correct work was shown.
Question 32
Geometry – Aug. ’23 [58]
Geometry – Aug. ’23 [19] [OVER]
Part III
Answer all 3 questions in this part. Each correct answer will receive 4 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided for each question to determine your answer.
Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct
numerical answer with no work shown will receive only 1 credit. All answers should be
written in pen, except for graphs and drawings, which should be done in pencil. [
12]
32 Josh is making a square-based fire pit out of concrete for his backyard, as modeled by the right
prism below. He plans to make the outside walls of the fire pit 3.5 feet on each side with a height
of 1.5 feet. The concrete walls of the re pit are going to be 9 inches thick.
9 in
3.5 ft
1.5 ft
If a bag of concrete mix will ll 0.6 ft
3
, determine and state the minimum number of bags needed
to build the re pit.
Score 0: The student did not show enough correct relevant course-level work to receive any credit.
Question 33
Geometry – Aug. ’23 [59]
Geometry – Aug. ’23 [20]
33 A telephone pole 11 meters tall needs to be stabilized with a support beam, as modeled below.
11 m
Support beam
Two conditions for proper support are:
• The beam reaches the telephone pole at 70% of the telephone pole’s height above the
ground.
• The beam forms a 65° angle with the ground.
Determine and state, to the nearest tenth of a meter, the length of the support beam that meets
these conditions for this telephone pole.
Determine and state, to the nearest tenth of a meter, how far the support beam must be placed
from the base of the pole to meet the conditions.
Geometry – Aug. ’23 [20]
33 A telephone pole 11 meters tall needs to be stabilized with a support beam, as modeled below.
11 m
Support beam
Two conditions for proper support are:
• The beam reaches the telephone pole at 70% of the telephone pole’s height above the
ground.
• The beam forms a 65° angle with the ground.
Determine and state, to the nearest tenth of a meter, the length of the support beam that meets
these conditions for this telephone pole.
Determine and state, to the nearest tenth of a meter, how far the support beam must be placed
from the base of the pole to meet the conditions.
Geometry – Aug. ’23 [20]
33 A telephone pole 11 meters tall needs to be stabilized with a support beam, as modeled below.
11 m
Support beam
Two conditions for proper support are:
• The beam reaches the telephone pole at 70% of the telephone pole’s height above the
ground.
• The beam forms a 65° angle with the ground.
Determine and state, to the nearest tenth of a meter, the length of the support beam that meets
these conditions for this telephone pole.
Determine and state, to the nearest tenth of a meter, how far the support beam must be placed
from the base of the pole to meet the conditions.
Score 4: The student gave a complete and correct response.
Question 33
Geometry – Aug. ’23 [60]
Geometry – Aug. ’23 [20]
33 A telephone pole 11 meters tall needs to be stabilized with a support beam, as modeled below.
11 m
Support beam
Two conditions for proper support are:
• The beam reaches the telephone pole at 70% of the telephone pole’s height above the
ground.
• The beam forms a 65° angle with the ground.
Determine and state, to the nearest tenth of a meter, the length of the support beam that meets
these conditions for this telephone pole.
Determine and state, to the nearest tenth of a meter, how far the support beam must be placed
from the base of the pole to meet the conditions.
Geometry – Aug. ’23 [20]
33 A telephone pole 11 meters tall needs to be stabilized with a support beam, as modeled below.
11 m
Support beam
Two conditions for proper support are:
• The beam reaches the telephone pole at 70% of the telephone pole’s height above the
ground.
• The beam forms a 65° angle with the ground.
Determine and state, to the nearest tenth of a meter, the length of the support beam that meets
these conditions for this telephone pole.
Determine and state, to the nearest tenth of a meter, how far the support beam must be placed
from the base of the pole to meet the conditions.
Geometry – Aug. ’23 [20]
33 A telephone pole 11 meters tall needs to be stabilized with a support beam, as modeled below.
11 m
Support beam
Two conditions for proper support are:
• The beam reaches the telephone pole at 70% of the telephone pole’s height above the
ground.
• The beam forms a 65° angle with the ground.
Determine and state, to the nearest tenth of a meter, the length of the support beam that meets
these conditions for this telephone pole.
Determine and state, to the nearest tenth of a meter, how far the support beam must be placed
from the base of the pole to meet the conditions.
Score 4: The student gave a complete and correct response.
Question 33
Geometry – Aug. ’23 [61]
Geometry – Aug. ’23 [20]
33 A telephone pole 11 meters tall needs to be stabilized with a support beam, as modeled below.
11 m
Support beam
Two conditions for proper support are:
• The beam reaches the telephone pole at 70% of the telephone pole’s height above the
ground.
• The beam forms a 65° angle with the ground.
Determine and state, to the nearest tenth of a meter, the length of the support beam that meets
these conditions for this telephone pole.
Determine and state, to the nearest tenth of a meter, how far the support beam must be placed
from the base of the pole to meet the conditions.
Geometry – Aug. ’23 [20]
33 A telephone pole 11 meters tall needs to be stabilized with a support beam, as modeled below.
11 m
Support beam
Two conditions for proper support are:
• The beam reaches the telephone pole at 70% of the telephone pole’s height above the
ground.
• The beam forms a 65° angle with the ground.
Determine and state, to the nearest tenth of a meter, the length of the support beam that meets
these conditions for this telephone pole.
Determine and state, to the nearest tenth of a meter, how far the support beam must be placed
from the base of the pole to meet the conditions.
Geometry – Aug. ’23 [20]
33 A telephone pole 11 meters tall needs to be stabilized with a support beam, as modeled below.
11 m
Support beam
Two conditions for proper support are:
• The beam reaches the telephone pole at 70% of the telephone pole’s height above the
ground.
• The beam forms a 65° angle with the ground.
Determine and state, to the nearest tenth of a meter, the length of the support beam that meets
these conditions for this telephone pole.
Determine and state, to the nearest tenth of a meter, how far the support beam must be placed
from the base of the pole to meet the conditions.
Score 4: The student gave a complete and correct response.
Question 33
Geometry – Aug. ’23 [62]
Geometry – Aug. ’23 [20]
33 A telephone pole 11 meters tall needs to be stabilized with a support beam, as modeled below.
11 m
Support beam
Two conditions for proper support are:
• The beam reaches the telephone pole at 70% of the telephone pole’s height above the
ground.
• The beam forms a 65° angle with the ground.
Determine and state, to the nearest tenth of a meter, the length of the support beam that meets
these conditions for this telephone pole.
Determine and state, to the nearest tenth of a meter, how far the support beam must be placed
from the base of the pole to meet the conditions.
Geometry – Aug. ’23 [20]
33 A telephone pole 11 meters tall needs to be stabilized with a support beam, as modeled below.
11 m
Support beam
Two conditions for proper support are:
• The beam reaches the telephone pole at 70% of the telephone pole’s height above the
ground.
• The beam forms a 65° angle with the ground.
Determine and state, to the nearest tenth of a meter, the length of the support beam that meets
these conditions for this telephone pole.
Determine and state, to the nearest tenth of a meter, how far the support beam must be placed
from the base of the pole to meet the conditions.
Geometry – Aug. ’23 [20]
33 A telephone pole 11 meters tall needs to be stabilized with a support beam, as modeled below.
11 m
Support beam
Two conditions for proper support are:
• The beam reaches the telephone pole at 70% of the telephone pole’s height above the
ground.
• The beam forms a 65° angle with the ground.
Determine and state, to the nearest tenth of a meter, the length of the support beam that meets
these conditions for this telephone pole.
Determine and state, to the nearest tenth of a meter, how far the support beam must be placed
from the base of the pole to meet the conditions.
Score 4: The student gave a complete and correct response.
Question 33
Geometry – Aug. ’23 [63]
Geometry – Aug. ’23 [20]
33 A telephone pole 11 meters tall needs to be stabilized with a support beam, as modeled below.
11 m
Support beam
Two conditions for proper support are:
• The beam reaches the telephone pole at 70% of the telephone pole’s height above the
ground.
• The beam forms a 65° angle with the ground.
Determine and state, to the nearest tenth of a meter, the length of the support beam that meets
these conditions for this telephone pole.
Determine and state, to the nearest tenth of a meter, how far the support beam must be placed
from the base of the pole to meet the conditions.
Geometry – Aug. ’23 [20]
33 A telephone pole 11 meters tall needs to be stabilized with a support beam, as modeled below.
11 m
Support beam
Two conditions for proper support are:
• The beam reaches the telephone pole at 70% of the telephone pole’s height above the
ground.
• The beam forms a 65° angle with the ground.
Determine and state, to the nearest tenth of a meter, the length of the support beam that meets
these conditions for this telephone pole.
Determine and state, to the nearest tenth of a meter, how far the support beam must be placed
from the base of the pole to meet the conditions.
Geometry – Aug. ’23 [20]
33 A telephone pole 11 meters tall needs to be stabilized with a support beam, as modeled below.
11 m
Support beam
Two conditions for proper support are:
• The beam reaches the telephone pole at 70% of the telephone pole’s height above the
ground.
• The beam forms a 65° angle with the ground.
Determine and state, to the nearest tenth of a meter, the length of the support beam that meets
these conditions for this telephone pole.
Determine and state, to the nearest tenth of a meter, how far the support beam must be placed
from the base of the pole to meet the conditions.
Score 3: The student used an incorrect height when determining the length of the support beam.
Question 33
Geometry – Aug. ’23 [64]
Geometry – Aug. ’23 [20]
33 A telephone pole 11 meters tall needs to be stabilized with a support beam, as modeled below.
11 m
Support beam
Two conditions for proper support are:
• The beam reaches the telephone pole at 70% of the telephone pole’s height above the
ground.
• The beam forms a 65° angle with the ground.
Determine and state, to the nearest tenth of a meter, the length of the support beam that meets
these conditions for this telephone pole.
Determine and state, to the nearest tenth of a meter, how far the support beam must be placed
from the base of the pole to meet the conditions.
Geometry – Aug. ’23 [20]
33 A telephone pole 11 meters tall needs to be stabilized with a support beam, as modeled below.
11 m
Support beam
Two conditions for proper support are:
• The beam reaches the telephone pole at 70% of the telephone pole’s height above the
ground.
• The beam forms a 65° angle with the ground.
Determine and state, to the nearest tenth of a meter, the length of the support beam that meets
these conditions for this telephone pole.
Determine and state, to the nearest tenth of a meter, how far the support beam must be placed
from the base of the pole to meet the conditions.
Geometry – Aug. ’23 [20]
33 A telephone pole 11 meters tall needs to be stabilized with a support beam, as modeled below.
11 m
Support beam
Two conditions for proper support are:
• The beam reaches the telephone pole at 70% of the telephone pole’s height above the
ground.
• The beam forms a 65° angle with the ground.
Determine and state, to the nearest tenth of a meter, the length of the support beam that meets
these conditions for this telephone pole.
Determine and state, to the nearest tenth of a meter, how far the support beam must be placed
from the base of the pole to meet the conditions.
Score 2: The student determined the length of the support beam, but no further correct work was
shown.
Question 33
Geometry – Aug. ’23 [65]
Geometry – Aug. ’23 [20]
33 A telephone pole 11 meters tall needs to be stabilized with a support beam, as modeled below.
11 m
Support beam
Two conditions for proper support are:
• The beam reaches the telephone pole at 70% of the telephone pole’s height above the
ground.
• The beam forms a 65° angle with the ground.
Determine and state, to the nearest tenth of a meter, the length of the support beam that meets
these conditions for this telephone pole.
Determine and state, to the nearest tenth of a meter, how far the support beam must be placed
from the base of the pole to meet the conditions.
Geometry – Aug. ’23 [20]
33 A telephone pole 11 meters tall needs to be stabilized with a support beam, as modeled below.
11 m
Support beam
Two conditions for proper support are:
• The beam reaches the telephone pole at 70% of the telephone pole’s height above the
ground.
• The beam forms a 65° angle with the ground.
Determine and state, to the nearest tenth of a meter, the length of the support beam that meets
these conditions for this telephone pole.
Determine and state, to the nearest tenth of a meter, how far the support beam must be placed
from the base of the pole to meet the conditions.
Geometry – Aug. ’23 [20]
33 A telephone pole 11 meters tall needs to be stabilized with a support beam, as modeled below.
11 m
Support beam
Two conditions for proper support are:
• The beam reaches the telephone pole at 70% of the telephone pole’s height above the
ground.
• The beam forms a 65° angle with the ground.
Determine and state, to the nearest tenth of a meter, the length of the support beam that meets
these conditions for this telephone pole.
Determine and state, to the nearest tenth of a meter, how far the support beam must be placed
from the base of the pole to meet the conditions.
Score 2: The student used an incorrect height and made a computational error when determining
the length of the support beam. The student found an appropriate distance from the
bottom of the support beam to the base of the pole.
Question 33
Geometry – Aug. ’23 [66]
Geometry – Aug. ’23 [20]
33 A telephone pole 11 meters tall needs to be stabilized with a support beam, as modeled below.
11 m
Support beam
Two conditions for proper support are:
• The beam reaches the telephone pole at 70% of the telephone pole’s height above the
ground.
• The beam forms a 65° angle with the ground.
Determine and state, to the nearest tenth of a meter, the length of the support beam that meets
these conditions for this telephone pole.
Determine and state, to the nearest tenth of a meter, how far the support beam must be placed
from the base of the pole to meet the conditions.
Geometry – Aug. ’23 [20]
33 A telephone pole 11 meters tall needs to be stabilized with a support beam, as modeled below.
11 m
Support beam
Two conditions for proper support are:
• The beam reaches the telephone pole at 70% of the telephone pole’s height above the
ground.
• The beam forms a 65° angle with the ground.
Determine and state, to the nearest tenth of a meter, the length of the support beam that meets
these conditions for this telephone pole.
Determine and state, to the nearest tenth of a meter, how far the support beam must be placed
from the base of the pole to meet the conditions.
Geometry – Aug. ’23 [20]
33 A telephone pole 11 meters tall needs to be stabilized with a support beam, as modeled below.
11 m
Support beam
Two conditions for proper support are:
• The beam reaches the telephone pole at 70% of the telephone pole’s height above the
ground.
• The beam forms a 65° angle with the ground.
Determine and state, to the nearest tenth of a meter, the length of the support beam that meets
these conditions for this telephone pole.
Determine and state, to the nearest tenth of a meter, how far the support beam must be placed
from the base of the pole to meet the conditions.
Score 1: The student used an incorrect height when determining the length of the support beam.
No further correct work was shown.
Question 33
Geometry – Aug. ’23 [67]
Geometry – Aug. ’23 [20]
33 A telephone pole 11 meters tall needs to be stabilized with a support beam, as modeled below.
11 m
Support beam
Two conditions for proper support are:
• The beam reaches the telephone pole at 70% of the telephone pole’s height above the
ground.
• The beam forms a 65° angle with the ground.
Determine and state, to the nearest tenth of a meter, the length of the support beam that meets
these conditions for this telephone pole.
Determine and state, to the nearest tenth of a meter, how far the support beam must be placed
from the base of the pole to meet the conditions.
Geometry – Aug. ’23 [20]
33 A telephone pole 11 meters tall needs to be stabilized with a support beam, as modeled below.
11 m
Support beam
Two conditions for proper support are:
• The beam reaches the telephone pole at 70% of the telephone pole’s height above the
ground.
• The beam forms a 65° angle with the ground.
Determine and state, to the nearest tenth of a meter, the length of the support beam that meets
these conditions for this telephone pole.
Determine and state, to the nearest tenth of a meter, how far the support beam must be placed
from the base of the pole to meet the conditions.
Geometry – Aug. ’23 [20]
33 A telephone pole 11 meters tall needs to be stabilized with a support beam, as modeled below.
11 m
Support beam
Two conditions for proper support are:
• The beam reaches the telephone pole at 70% of the telephone pole’s height above the
ground.
• The beam forms a 65° angle with the ground.
Determine and state, to the nearest tenth of a meter, the length of the support beam that meets
these conditions for this telephone pole.
Determine and state, to the nearest tenth of a meter, how far the support beam must be placed
from the base of the pole to meet the conditions.
Score 1: The student wrote one correct relevant trigonometric equation.
Question 33
Geometry – Aug. ’23 [68]
Geometry – Aug. ’23 [20]
33 A telephone pole 11 meters tall needs to be stabilized with a support beam, as modeled below.
11 m
Support beam
Two conditions for proper support are:
• The beam reaches the telephone pole at 70% of the telephone pole’s height above the
ground.
• The beam forms a 65° angle with the ground.
Determine and state, to the nearest tenth of a meter, the length of the support beam that meets
these conditions for this telephone pole.
Determine and state, to the nearest tenth of a meter, how far the support beam must be placed
from the base of the pole to meet the conditions.
Geometry – Aug. ’23 [20]
33 A telephone pole 11 meters tall needs to be stabilized with a support beam, as modeled below.
11 m
Support beam
Two conditions for proper support are:
• The beam reaches the telephone pole at 70% of the telephone pole’s height above the
ground.
• The beam forms a 65° angle with the ground.
Determine and state, to the nearest tenth of a meter, the length of the support beam that meets
these conditions for this telephone pole.
Determine and state, to the nearest tenth of a meter, how far the support beam must be placed
from the base of the pole to meet the conditions.
Geometry – Aug. ’23 [20]
33 A telephone pole 11 meters tall needs to be stabilized with a support beam, as modeled below.
11 m
Support beam
Two conditions for proper support are:
• The beam reaches the telephone pole at 70% of the telephone pole’s height above the
ground.
• The beam forms a 65° angle with the ground.
Determine and state, to the nearest tenth of a meter, the length of the support beam that meets
these conditions for this telephone pole.
Determine and state, to the nearest tenth of a meter, how far the support beam must be placed
from the base of the pole to meet the conditions.
Score 0: The student did not show enough correct relevant course-level work to receive any credit.
Question 34
Geometry – Aug. ’23 [69]
Geometry – Aug. ’23 [21] [OVER]
34 The coordinates of the vertices of quadrilateral ABCD are A(0,4), B(3,8), C(8,3), and D(5,21).
Prove that ABCD is a parallelogram, but not a rectangle.
[The use of the set of axes below is optional.]
y
x
Geometry – Aug. ’23 [21] [OVER]
34 The coordinates of the vertices of quadrilateral ABCD are A(0,4), B(3,8), C(8,3), and D(5,21).
Prove that ABCD is a parallelogram, but not a rectangle.
[The use of the set of axes below is optional.]
y
x
Score 4: The student gave a complete and correct response.
Question 34
Geometry – Aug. ’23 [70]
Geometry – Aug. ’23 [21] [OVER]
34 The coordinates of the vertices of quadrilateral ABCD are A(0,4), B(3,8), C(8,3), and D(5,21).
Prove that ABCD is a parallelogram, but not a rectangle.
[The use of the set of axes below is optional.]
y
x
Geometry – Aug. ’23 [21] [OVER]
34 The coordinates of the vertices of quadrilateral ABCD are A(0,4), B(3,8), C(8,3), and D(5,21).
Prove that ABCD is a parallelogram, but not a rectangle.
[The use of the set of axes below is optional.]
y
x
Score 4: The student gave a complete and correct response.
Question 34
Geometry – Aug. ’23 [71]
Geometry – Aug. ’23 [21] [OVER]
34 The coordinates of the vertices of quadrilateral ABCD are A(0,4), B(3,8), C(8,3), and D(5,21).
Prove that ABCD is a parallelogram, but not a rectangle.
[The use of the set of axes below is optional.]
y
x
Geometry – Aug. ’23 [21] [OVER]
34 The coordinates of the vertices of quadrilateral ABCD are A(0,4), B(3,8), C(8,3), and D(5,21).
Prove that ABCD is a parallelogram, but not a rectangle.
[The use of the set of axes below is optional.]
y
x
Score 3: The student did not write a concluding statement when proving ABCD is not a rectangle.
Question 34
Geometry – Aug. ’23 [72]
Geometry – Aug. ’23 [21] [OVER]
34 The coordinates of the vertices of quadrilateral ABCD are A(0,4), B(3,8), C(8,3), and D(5,21).
Prove that ABCD is a parallelogram, but not a rectangle.
[The use of the set of axes below is optional.]
y
x
Geometry – Aug. ’23 [21] [OVER]
34 The coordinates of the vertices of quadrilateral ABCD are A(0,4), B(3,8), C(8,3), and D(5,21).
Prove that ABCD is a parallelogram, but not a rectangle.
[The use of the set of axes below is optional.]
y
x
Score 2: The student proved ABCD was not a rectangle, but did not prove ABCD was a
parallelogram.
Question 34
Geometry – Aug. ’23 [73]
Geometry – Aug. ’23 [21] [OVER]
34 The coordinates of the vertices of quadrilateral ABCD are A(0,4), B(3,8), C(8,3), and D(5,21).
Prove that ABCD is a parallelogram, but not a rectangle.
[The use of the set of axes below is optional.]
y
x
Geometry – Aug. ’23 [21] [OVER]
34 The coordinates of the vertices of quadrilateral ABCD are A(0,4), B(3,8), C(8,3), and D(5,21).
Prove that ABCD is a parallelogram, but not a rectangle.
[The use of the set of axes below is optional.]
y
x
Score 2: The student proved ABCD was not a rectangle, but did not prove ABCD was a
parallelogram.
Question 34
Geometry – Aug. ’23 [74]
Geometry – Aug. ’23 [21] [OVER]
34 The coordinates of the vertices of quadrilateral ABCD are A(0,4), B(3,8), C(8,3), and D(5,21).
Prove that ABCD is a parallelogram, but not a rectangle.
[The use of the set of axes below is optional.]
y
x
Geometry – Aug. ’23 [21] [OVER]
34 The coordinates of the vertices of quadrilateral ABCD are A(0,4), B(3,8), C(8,3), and D(5,21).
Prove that ABCD is a parallelogram, but not a rectangle.
[The use of the set of axes below is optional.]
y
x
Score 2: The student proved ABCD was a parallelogram, but did not prove ABCD was not a
rectangle.
Question 34
Geometry – Aug. ’23 [75]
Geometry – Aug. ’23 [21] [OVER]
34 The coordinates of the vertices of quadrilateral ABCD are A(0,4), B(3,8), C(8,3), and D(5,21).
Prove that ABCD is a parallelogram, but not a rectangle.
[The use of the set of axes below is optional.]
y
x
Geometry – Aug. ’23 [21] [OVER]
34 The coordinates of the vertices of quadrilateral ABCD are A(0,4), B(3,8), C(8,3), and D(5,21).
Prove that ABCD is a parallelogram, but not a rectangle.
[The use of the set of axes below is optional.]
y
x
Score 1: The student found the length of all four sides, but no further correct work was shown.
Question 34
Geometry – Aug. ’23 [76]
Geometry – Aug. ’23 [21] [OVER]
34 The coordinates of the vertices of quadrilateral ABCD are A(0,4), B(3,8), C(8,3), and D(5,21).
Prove that ABCD is a parallelogram, but not a rectangle.
[The use of the set of axes below is optional.]
y
x
Geometry – Aug. ’23 [21] [OVER]
34 The coordinates of the vertices of quadrilateral ABCD are A(0,4), B(3,8), C(8,3), and D(5,21).
Prove that ABCD is a parallelogram, but not a rectangle.
[The use of the set of axes below is optional.]
y
x
Score 1: The student found the slopes of all four sides, but wrote an incomplete concluding
statement when proving ABCD was not a rectangle.
Question 34
Geometry – Aug. ’23 [77]
Geometry – Aug. ’23 [21] [OVER]
34 The coordinates of the vertices of quadrilateral ABCD are A(0,4), B(3,8), C(8,3), and D(5,21).
Prove that ABCD is a parallelogram, but not a rectangle.
[The use of the set of axes below is optional.]
y
x
Geometry – Aug. ’23 [21] [OVER]
34 The coordinates of the vertices of quadrilateral ABCD are A(0,4), B(3,8), C(8,3), and D(5,21).
Prove that ABCD is a parallelogram, but not a rectangle.
[The use of the set of axes below is optional.]
y
x
Score 1: The student found the midpoints of both diagonals, but wrote an incomplete concluding
statement when proving ABCD was a parallelogram. No further correct work was shown.
Question 34
Geometry – Aug. ’23 [78]
Geometry – Aug. ’23 [21] [OVER]
34 The coordinates of the vertices of quadrilateral ABCD are A(0,4), B(3,8), C(8,3), and D(5,21).
Prove that ABCD is a parallelogram, but not a rectangle.
[The use of the set of axes below is optional.]
y
x
Geometry – Aug. ’23 [21] [OVER]
34 The coordinates of the vertices of quadrilateral ABCD are A(0,4), B(3,8), C(8,3), and D(5,21).
Prove that ABCD is a parallelogram, but not a rectangle.
[The use of the set of axes below is optional.]
y
x
Score 0: The student did not show enough correct relevant work to receive any credit.
Question 34
Geometry – Aug. ’23 [79]
Geometry – Aug. ’23 [21] [OVER]
34 The coordinates of the vertices of quadrilateral ABCD are A(0,4), B(3,8), C(8,3), and D(5,21).
Prove that ABCD is a parallelogram, but not a rectangle.
[The use of the set of axes below is optional.]
y
x
Geometry – Aug. ’23 [21] [OVER]
34 The coordinates of the vertices of quadrilateral ABCD are A(0,4), B(3,8), C(8,3), and D(5,21).
Prove that ABCD is a parallelogram, but not a rectangle.
[The use of the set of axes below is optional.]
y
x
Score 0: The student did not show enough correct relevant work to receive any credit.
Question 34
Geometry – Aug. ’23 [80]
Geometry – Aug. ’23 [21] [OVER]
34 The coordinates of the vertices of quadrilateral ABCD are A(0,4), B(3,8), C(8,3), and D(5,21).
Prove that ABCD is a parallelogram, but not a rectangle.
[The use of the set of axes below is optional.]
y
x
Geometry – Aug. ’23 [21] [OVER]
34 The coordinates of the vertices of quadrilateral ABCD are A(0,4), B(3,8), C(8,3), and D(5,21).
Prove that ABCD is a parallelogram, but not a rectangle.
[The use of the set of axes below is optional.]
y
x
Score 0: The student did not show enough correct relevant work to receive any credit.
Question 35
Geometry – Aug. ’23 [81]
Geometry – Aug. ’23 [22]
Part IV
Answer the question in this part. A correct answer will receive 6 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided to determine your answer. Note that diagrams are
not necessarily drawn to scale. A correct numerical answer with no work shown will receive
only 1 credit. All answers should be written in pen, except for graphs and drawings, which
should be done in pencil. [
6]
35 In the diagram below of quadrilateral FACT,
BR
intersects diagonal
AT
at E,
AF
||
CT
, and
AF
>
CT
.
F R
E
T
A B
C
Prove: (AB)(TE) 5 (AE)(TR)
Work space for question 35 is continued on the next page.
Geometry – Aug. ’23 [22]
Part IV
Answer the question in this part. A correct answer will receive 6 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided to determine your answer. Note that diagrams are
not necessarily drawn to scale. A correct numerical answer with no work shown will receive
only 1 credit. All answers should be written in pen, except for graphs and drawings, which
should be done in pencil. [
6]
35 In the diagram below of quadrilateral FACT,
BR
intersects diagonal
AT
at E,
AF
||
CT
, and
AF
>
CT
.
F R
E
T
A B
C
Prove: (AB)(TE) 5 (AE)(TR)
Work space for question 35 is continued on the next page.
Score 6: The student gave a complete and correct response.
Question 35
Geometry – Aug. ’23 [82]
Geometry – Aug. ’23 [22]
Part IV
Answer the question in this part. A correct answer will receive 6 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided to determine your answer. Note that diagrams are
not necessarily drawn to scale. A correct numerical answer with no work shown will receive
only 1 credit. All answers should be written in pen, except for graphs and drawings, which
should be done in pencil. [
6]
35 In the diagram below of quadrilateral FACT,
BR
intersects diagonal
AT
at E,
AF
||
CT
, and
AF
>
CT
.
F R
E
T
A B
C
Prove: (AB)(TE) 5 (AE)(TR)
Work space for question 35 is continued on the next page.
Geometry – Aug. ’23 [22]
Part IV
Answer the question in this part. A correct answer will receive 6 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided to determine your answer. Note that diagrams are
not necessarily drawn to scale. A correct numerical answer with no work shown will receive
only 1 credit. All answers should be written in pen, except for graphs and drawings, which
should be done in pencil. [
6]
35 In the diagram below of quadrilateral FACT,
BR
intersects diagonal
AT
at E,
AF
||
CT
, and
AF
>
CT
.
F R
E
T
A B
C
Prove: (AB)(TE) 5 (AE)(TR)
Work space for question 35 is continued on the next page.
Score 6: The student gave a complete and correct response.
Question 35
Geometry – Aug. ’23 [83]
Geometry – Aug. ’23 [22]
Part IV
Answer the question in this part. A correct answer will receive 6 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided to determine your answer. Note that diagrams are
not necessarily drawn to scale. A correct numerical answer with no work shown will receive
only 1 credit. All answers should be written in pen, except for graphs and drawings, which
should be done in pencil. [
6]
35 In the diagram below of quadrilateral FACT,
BR
intersects diagonal
AT
at E,
AF
||
CT
, and
AF
>
CT
.
F R
E
T
A B
C
Prove: (AB)(TE) 5 (AE)(TR)
Work space for question 35 is continued on the next page.
Geometry – Aug. ’23 [22]
Part IV
Answer the question in this part. A correct answer will receive 6 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided to determine your answer. Note that diagrams are
not necessarily drawn to scale. A correct numerical answer with no work shown will receive
only 1 credit. All answers should be written in pen, except for graphs and drawings, which
should be done in pencil. [
6]
35 In the diagram below of quadrilateral FACT,
BR
intersects diagonal
AT
at E,
AF
||
CT
, and
AF
>
CT
.
F R
E
T
A B
C
Prove: (AB)(TE) 5 (AE)(TR)
Work space for question 35 is continued on the next page.
Score 6: The student gave a complete and correct response.
Question 35
Geometry – Aug. ’23 [84]
Geometry – Aug. ’23 [22]
Part IV
Answer the question in this part. A correct answer will receive 6 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided to determine your answer. Note that diagrams are
not necessarily drawn to scale. A correct numerical answer with no work shown will receive
only 1 credit. All answers should be written in pen, except for graphs and drawings, which
should be done in pencil. [
6]
35 In the diagram below of quadrilateral FACT,
BR
intersects diagonal
AT
at E,
AF
||
CT
, and
AF
>
CT
.
F R
E
T
A B
C
Prove: (AB)(TE) 5 (AE)(TR)
Work space for question 35 is continued on the next page.
Geometry – Aug. ’23 [22]
Part IV
Answer the question in this part. A correct answer will receive 6 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided to determine your answer. Note that diagrams are
not necessarily drawn to scale. A correct numerical answer with no work shown will receive
only 1 credit. All answers should be written in pen, except for graphs and drawings, which
should be done in pencil. [
6]
35 In the diagram below of quadrilateral FACT,
BR
intersects diagonal
AT
at E,
AF
||
CT
, and
AF
>
CT
.
F R
E
T
A B
C
Prove: (AB)(TE) 5 (AE)(TR)
Work space for question 35 is continued on the next page.
Score 5: The student had an incorrect reason in step 9.
Question 35
Geometry – Aug. ’23 [85]
Geometry – Aug. ’23 [22]
Part IV
Answer the question in this part. A correct answer will receive 6 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided to determine your answer. Note that diagrams are
not necessarily drawn to scale. A correct numerical answer with no work shown will receive
only 1 credit. All answers should be written in pen, except for graphs and drawings, which
should be done in pencil. [
6]
35 In the diagram below of quadrilateral FACT,
BR
intersects diagonal
AT
at E,
AF
||
CT
, and
AF
>
CT
.
F R
E
T
A B
C
Prove: (AB)(TE) 5 (AE)(TR)
Work space for question 35 is continued on the next page.
Geometry – Aug. ’23 [22]
Part IV
Answer the question in this part. A correct answer will receive 6 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided to determine your answer. Note that diagrams are
not necessarily drawn to scale. A correct numerical answer with no work shown will receive
only 1 credit. All answers should be written in pen, except for graphs and drawings, which
should be done in pencil. [
6]
35 In the diagram below of quadrilateral FACT,
BR
intersects diagonal
AT
at E,
AF
||
CT
, and
AF
>
CT
.
F R
E
T
A B
C
Prove: (AB)(TE) 5 (AE)(TR)
Work space for question 35 is continued on the next page.
Score 4: The student made one conceptual error by not proving FACT was a parallelogram.
Question 35
Geometry – Aug. ’23 [86]
Geometry – Aug. ’23 [22]
Part IV
Answer the question in this part. A correct answer will receive 6 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided to determine your answer. Note that diagrams are
not necessarily drawn to scale. A correct numerical answer with no work shown will receive
only 1 credit. All answers should be written in pen, except for graphs and drawings, which
should be done in pencil. [
6]
35 In the diagram below of quadrilateral FACT,
BR
intersects diagonal
AT
at E,
AF
||
CT
, and
AF
>
CT
.
F R
E
T
A B
C
Prove: (AB)(TE) 5 (AE)(TR)
Work space for question 35 is continued on the next page.
Geometry – Aug. ’23 [22]
Part IV
Answer the question in this part. A correct answer will receive 6 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided to determine your answer. Note that diagrams are
not necessarily drawn to scale. A correct numerical answer with no work shown will receive
only 1 credit. All answers should be written in pen, except for graphs and drawings, which
should be done in pencil. [
6]
35 In the diagram below of quadrilateral FACT,
BR
intersects diagonal
AT
at E,
AF
||
CT
, and
AF
>
CT
.
F R
E
T
A B
C
Prove: (AB)(TE) 5 (AE)(TR)
Work space for question 35 is continued on the next page.
Score 4: The student had incorrect reasons for steps 6 and 7.
Question 35
Geometry – Aug. ’23 [87]
Geometry – Aug. ’23 [22]
Part IV
Answer the question in this part. A correct answer will receive 6 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided to determine your answer. Note that diagrams are
not necessarily drawn to scale. A correct numerical answer with no work shown will receive
only 1 credit. All answers should be written in pen, except for graphs and drawings, which
should be done in pencil. [
6]
35 In the diagram below of quadrilateral FACT,
BR
intersects diagonal
AT
at E,
AF
||
CT
, and
AF
>
CT
.
F R
E
T
A B
C
Prove: (AB)(TE) 5 (AE)(TR)
Work space for question 35 is continued on the next page.
Geometry – Aug. ’23 [22]
Part IV
Answer the question in this part. A correct answer will receive 6 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided to determine your answer. Note that diagrams are
not necessarily drawn to scale. A correct numerical answer with no work shown will receive
only 1 credit. All answers should be written in pen, except for graphs and drawings, which
should be done in pencil. [
6]
35 In the diagram below of quadrilateral FACT,
BR
intersects diagonal
AT
at E,
AF
||
CT
, and
AF
>
CT
.
F R
E
T
A B
C
Prove: (AB)(TE) 5 (AE)(TR)
Work space for question 35 is continued on the next page.
Score 4: The student had an incorrect reason in step 2 and an incomplete reason in step 4.
Question 35
Geometry – Aug. ’23 [88]
Geometry – Aug. ’23 [22]
Part IV
Answer the question in this part. A correct answer will receive 6 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided to determine your answer. Note that diagrams are
not necessarily drawn to scale. A correct numerical answer with no work shown will receive
only 1 credit. All answers should be written in pen, except for graphs and drawings, which
should be done in pencil. [
6]
35 In the diagram below of quadrilateral FACT,
BR
intersects diagonal
AT
at E,
AF
||
CT
, and
AF
>
CT
.
F R
E
T
A B
C
Prove: (AB)(TE) 5 (AE)(TR)
Work space for question 35 is continued on the next page.
Geometry – Aug. ’23 [22]
Part IV
Answer the question in this part. A correct answer will receive 6 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided to determine your answer. Note that diagrams are
not necessarily drawn to scale. A correct numerical answer with no work shown will receive
only 1 credit. All answers should be written in pen, except for graphs and drawings, which
should be done in pencil. [
6]
35 In the diagram below of quadrilateral FACT,
BR
intersects diagonal
AT
at E,
AF
||
CT
, and
AF
>
CT
.
F R
E
T
A B
C
Prove: (AB)(TE) 5 (AE)(TR)
Work space for question 35 is continued on the next page.
Score 3: The student had three incorrect statements and/or reasons after step 5.
Question 35
Geometry – Aug. ’23 [89]
Geometry – Aug. ’23 [22]
Part IV
Answer the question in this part. A correct answer will receive 6 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided to determine your answer. Note that diagrams are
not necessarily drawn to scale. A correct numerical answer with no work shown will receive
only 1 credit. All answers should be written in pen, except for graphs and drawings, which
should be done in pencil. [
6]
35 In the diagram below of quadrilateral FACT,
BR
intersects diagonal
AT
at E,
AF
||
CT
, and
AF
>
CT
.
F R
E
T
A B
C
Prove: (AB)(TE) 5 (AE)(TR)
Work space for question 35 is continued on the next page.
Geometry – Aug. ’23 [22]
Part IV
Answer the question in this part. A correct answer will receive 6 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided to determine your answer. Note that diagrams are
not necessarily drawn to scale. A correct numerical answer with no work shown will receive
only 1 credit. All answers should be written in pen, except for graphs and drawings, which
should be done in pencil. [
6]
35 In the diagram below of quadrilateral FACT,
BR
intersects diagonal
AT
at E,
AF
||
CT
, and
AF
>
CT
.
F R
E
T
A B
C
Prove: (AB)(TE) 5 (AE)(TR)
Work space for question 35 is continued on the next page.
Score 2: The student had two correct relevant statements and reasons in steps 2 and 3.
Question 35
Geometry – Aug. ’23 [90]
Geometry – Aug. ’23 [22]
Part IV
Answer the question in this part. A correct answer will receive 6 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided to determine your answer. Note that diagrams are
not necessarily drawn to scale. A correct numerical answer with no work shown will receive
only 1 credit. All answers should be written in pen, except for graphs and drawings, which
should be done in pencil. [
6]
35 In the diagram below of quadrilateral FACT,
BR
intersects diagonal
AT
at E,
AF
||
CT
, and
AF
>
CT
.
F R
E
T
A B
C
Prove: (AB)(TE) 5 (AE)(TR)
Work space for question 35 is continued on the next page.
Geometry – Aug. ’23 [22]
Part IV
Answer the question in this part. A correct answer will receive 6 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided to determine your answer. Note that diagrams are
not necessarily drawn to scale. A correct numerical answer with no work shown will receive
only 1 credit. All answers should be written in pen, except for graphs and drawings, which
should be done in pencil. [
6]
35 In the diagram below of quadrilateral FACT,
BR
intersects diagonal
AT
at E,
AF
||
CT
, and
AF
>
CT
.
F R
E
T
A B
C
Prove: (AB)(TE) 5 (AE)(TR)
Work space for question 35 is continued on the next page.
Score 1: The student had only one correct relevant statement and reason in step 5.
Question 35
Geometry – Aug. ’23 [91]
Geometry – Aug. ’23 [22]
Part IV
Answer the question in this part. A correct answer will receive 6 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided to determine your answer. Note that diagrams are
not necessarily drawn to scale. A correct numerical answer with no work shown will receive
only 1 credit. All answers should be written in pen, except for graphs and drawings, which
should be done in pencil. [
6]
35 In the diagram below of quadrilateral FACT,
BR
intersects diagonal
AT
at E,
AF
||
CT
, and
AF
>
CT
.
F R
E
T
A B
C
Prove: (AB)(TE) 5 (AE)(TR)
Work space for question 35 is continued on the next page.
Geometry – Aug. ’23 [22]
Part IV
Answer the question in this part. A correct answer will receive 6 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided to determine your answer. Note that diagrams are
not necessarily drawn to scale. A correct numerical answer with no work shown will receive
only 1 credit. All answers should be written in pen, except for graphs and drawings, which
should be done in pencil. [
6]
35 In the diagram below of quadrilateral FACT,
BR
intersects diagonal
AT
at E,
AF
||
CT
, and
AF
>
CT
.
F R
E
T
A B
C
Prove: (AB)(TE) 5 (AE)(TR)
Work space for question 35 is continued on the next page.
Score 1: The student had only one correct relevant statement and reason in step 2.
Question 35
Geometry – Aug. ’23 [92]
Geometry – Aug. ’23 [22]
Part IV
Answer the question in this part. A correct answer will receive 6 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided to determine your answer. Note that diagrams are
not necessarily drawn to scale. A correct numerical answer with no work shown will receive
only 1 credit. All answers should be written in pen, except for graphs and drawings, which
should be done in pencil. [
6]
35 In the diagram below of quadrilateral FACT,
BR
intersects diagonal
AT
at E,
AF
||
CT
, and
AF
>
CT
.
F R
E
T
A B
C
Prove: (AB)(TE) 5 (AE)(TR)
Work space for question 35 is continued on the next page.
Geometry – Aug. ’23 [22]
Part IV
Answer the question in this part. A correct answer will receive 6 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided to determine your answer. Note that diagrams are
not necessarily drawn to scale. A correct numerical answer with no work shown will receive
only 1 credit. All answers should be written in pen, except for graphs and drawings, which
should be done in pencil. [
6]
35 In the diagram below of quadrilateral FACT,
BR
intersects diagonal
AT
at E,
AF
||
CT
, and
AF
>
CT
.
F R
E
T
A B
C
Prove: (AB)(TE) 5 (AE)(TR)
Work space for question 35 is continued on the next page.
Score 1: The student had only one correct relevant statement and reason in step 2.
Question 35
Geometry – Aug. ’23 [93]
Geometry – Aug. ’23 [22]
Part IV
Answer the question in this part. A correct answer will receive 6 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided to determine your answer. Note that diagrams are
not necessarily drawn to scale. A correct numerical answer with no work shown will receive
only 1 credit. All answers should be written in pen, except for graphs and drawings, which
should be done in pencil. [
6]
35 In the diagram below of quadrilateral FACT,
BR
intersects diagonal
AT
at E,
AF
||
CT
, and
AF
>
CT
.
F R
E
T
A B
C
Prove: (AB)(TE) 5 (AE)(TR)
Work space for question 35 is continued on the next page.
Geometry – Aug. ’23 [22]
Part IV
Answer the question in this part. A correct answer will receive 6 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided to determine your answer. Note that diagrams are
not necessarily drawn to scale. A correct numerical answer with no work shown will receive
only 1 credit. All answers should be written in pen, except for graphs and drawings, which
should be done in pencil. [
6]
35 In the diagram below of quadrilateral FACT,
BR
intersects diagonal
AT
at E,
AF
||
CT
, and
AF
>
CT
.
F R
E
T
A B
C
Prove: (AB)(TE) 5 (AE)(TR)
Work space for question 35 is continued on the next page.
Score 0: The student did not show enough correct relevant work to receive any credit.
