The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
GEOMETRY
Wednesday, January 23, 2019 — 9:15 a.m. to 12:15 p.m.
MODEL RESPONSE SET
Table of Contents
Question 25 . . . . . . . . . . . . . . . . . . . 2
Question 26 . . . . . . . . . . . . . . . . . . . 8
Question 27 . . . . . . . . . . . . . . . . . . 14
Question 28 . . . . . . . . . . . . . . . . . . 18
Question 29 . . . . . . . . . . . . . . . . . . 26
Question 30 . . . . . . . . . . . . . . . . . . 32
Question 31 . . . . . . . . . . . . . . . . . . 37
Question 32 . . . . . . . . . . . . . . . . . . 45
Question 33 . . . . . . . . . . . . . . . . . . 54
Question 34 . . . . . . . . . . . . . . . . . . 62
Question 35 . . . . . . . . . . . . . . . . . . 70
Question 25
Geometry – Jan. ’19 [2]
25 Write an equation of the line that is parallel to the line whose equation is 3y 7 2x and passes
through the point (2,6).
Score 2: The student gave a complete and correct response.
Question 25
Geometry – Jan. ’19 [3]
25 Write an equation of the line that is parallel to the line whose equation is 3y 7 2x and passes
through the point (2,6).
Score 2: The student gave a complete and correct response.
Question 25
Geometry – Jan. ’19 [4]
25 Write an equation of the line that is parallel to the line whose equation is 3y 7 2x and passes
through the point (2,6).
Score 1: The student made an error in determining the y-intercept.
Question 25
Geometry – Jan. ’19 [5]
25 Write an equation of the line that is parallel to the line whose equation is 3y 7 2x and passes
through the point (2,6).
Score 1: The student made one rounding error in determining the y-intercept.
Question 25
Geometry – Jan. ’19 [6]
25 Write an equation of the line that is parallel to the line whose equation is 3y 7 2x and passes
through the point (2,6).
Score 1: The student made an error using the y-coordinate of the given point as the y-intercept.
Question 25
Geometry – Jan. ’19 [7]
25 Write an equation of the line that is parallel to the line whose equation is 3y 7 2x and passes
through the point (2,6).
Score 0: The student did not show enough correct relevant work to receive any credit.
Geometry – Jan. ’19 [8]
Question 26
26 Parallelogram ABCD is adjacent to rhombus DEFG, as shown below, and intersects
at H.
If m∠B 118° and m∠AHC 138°, determine and state m∠GFH.
B
C
A
G
H
D
FE
FC AGD
Score 2: The student gave a complete and correct response.
Geometry – Jan. ’19 [9]
Question 26
26 Parallelogram ABCD is adjacent to rhombus DEFG, as shown below, and intersects
at H.
If m∠B 118° and m∠AHC 138°, determine and state m∠GFH.
B
C
A
G
H
D
FE
FC AGD
Score 2: The student gave a complete and correct response.
Geometry – Jan. ’19 [10]
Question 26
26 Parallelogram ABCD is adjacent to rhombus DEFG, as shown below, and intersects
at H.
If m∠B 118° and m∠AHC 138°, determine and state m∠GFH.
B
C
A
G
H
D
FE
FC AGD
Score 2: The student gave a complete and correct response.
Geometry – Jan. ’19 [11]
Question 26
26 Parallelogram ABCD is adjacent to rhombus DEFG, as shown below, and intersects
at H.
If m∠B 118° and m∠AHC 138°, determine and state m∠GFH.
B
C
A
G
H
D
FE
FC AGD
Score 1: The student made an error that bisects ∠BCD.
CF
Geometry – Jan. ’19 [12]
Question 26
26 Parallelogram ABCD is adjacent to rhombus DEFG, as shown below, and intersects
at H.
If m∠B 118° and m∠AHC 138°, determine and state m∠GFH.
B
C
A
G
H
D
FE
FC AGD
Score 1: The student made a computational error in determining m∠CHD.
Geometry – Jan. ’19 [13]
Question 26
26 Parallelogram ABCD is adjacent to rhombus DEFG, as shown below, and intersects
at H.
If m∠B 118° and m∠AHC 138°, determine and state m∠GFH.
B
C
A
G
H
D
FE
FC AGD
Score 0: The student did not show enough correct relevant work to receive any credit.
Geometry – Jan. ’19 [14]
Question 27
27 As shown in the diagram below, secants PWR
––––>
and PTS
–––>
are drawn to circle O from external point P.
If m∠RPS 35°and m 121°, determine and state m .
RS
WT
R
P
T
W
S
O
Score 2: The student gave a complete and correct response.
Geometry – Jan. ’19 [15]
Question 27
27 As shown in the diagram below, secants PWR
––––>
and PTS
–––>
are drawn to circle O from external point P.
If m∠RPS 35°and m 121°, determine and state m .
RS
WT
R
P
T
W
S
O
Score 2: The student gave a complete and correct response.
Geometry – Jan. ’19 [16]
Question 27
27 As shown in the diagram below, secants PWR
––––>
and PTS
–––>
are drawn to circle O from external point P.
If m∠RPS 35°and m 121°, determine and state m .
RS
WT
R
P
T
W
S
O
Score 1: The student wrote a correct equation.
Geometry – Jan. ’19 [17]
Question 27
27 As shown in the diagram below, secants PWR
––––>
and PTS
–––>
are drawn to circle O from external point P.
If m∠RPS 35°and m 121°, determine and state m .
RS
WT
R
P
T
W
S
O
Score 0: The student gave a completely incorrect response.
Geometry – Jan. ’19 [18]
Question 28
28 On the set of axes below, rABC is graphed with coordinates A(2,1), B(3,1), and C(2,4).
Triangle QRS, the image of rABC, is graphed with coordinates Q(5,2), R(5,7), and S(8,2).
Describe a sequence of transformations that would map rABC onto rQRS.
B
S
Q
R
A
C
y
x
Score 2: The student gave a complete and correct response.
Geometry – Jan. ’19 [19]
Question 28
28 On the set of axes below, rABC is graphed with coordinates A(2,1), B(3,1), and C(2,4).
Triangle QRS, the image of rABC, is graphed with coordinates Q(5,2), R(5,7), and S(8,2).
Describe a sequence of transformations that would map rABC onto rQRS.
B
S
Q
R
A
C
y
x
Score 2: The student gave a complete and correct response.
Geometry – Jan. ’19 [20]
Question 28
28 On the set of axes below, rABC is graphed with coordinates A(2,1), B(3,1), and C(2,4).
Triangle QRS, the image of rABC, is graphed with coordinates Q(5,2), R(5,7), and S(8,2).
Describe a sequence of transformations that would map rABC onto rQRS.
B
S
Q
R
A
C
y
x
Score 2: The student gave a complete and correct response.
Geometry – Jan. ’19 [21]
Question 28
28 On the set of axes below, rABC is graphed with coordinates A(2,1), B(3,1), and C(2,4).
Triangle QRS, the image of rABC, is graphed with coordinates Q(5,2), R(5,7), and S(8,2).
Describe a sequence of transformations that would map rABC onto rQRS.
B
S
Q
R
A
C
y
x
Score 2: The student gave a complete and correct response.
Geometry – Jan. ’19 [22]
Question 28
28 On the set of axes below, rABC is graphed with coordinates A(2,1), B(3,1), and C(2,4).
Triangle QRS, the image of rABC, is graphed with coordinates Q(5,2), R(5,7), and S(8,2).
Describe a sequence of transformations that would map rABC onto rQRS.
B
S
Q
R
A
C
y
x
Score 1: The student did not state the center of rotation.
Geometry – Jan. ’19 [23]
Question 28
28 On the set of axes below, rABC is graphed with coordinates A(2,1), B(3,1), and C(2,4).
Triangle QRS, the image of rABC, is graphed with coordinates Q(5,2), R(5,7), and S(8,2).
Describe a sequence of transformations that would map rABC onto rQRS.
B
S
Q
R
A
C
y
x
Score 1: The student wrote an incorrect line of reflection.
Geometry – Jan. ’19 [24]
Question 28
28 On the set of axes below, rABC is graphed with coordinates A(2,1), B(3,1), and C(2,4).
Triangle QRS, the image of rABC, is graphed with coordinates Q(5,2), R(5,7), and S(8,2).
Describe a sequence of transformations that would map rABC onto rQRS.
B
S
Q
R
A
C
y
x
Score 1: The student demonstrated the sequence graphically and wrote an appropriate sequence
of transformations, but no specific description was written.
Geometry – Jan. ’19 [25]
Question 28
28 On the set of axes below, rABC is graphed with coordinates A(2,1), B(3,1), and C(2,4).
Triangle QRS, the image of rABC, is graphed with coordinates Q(5,2), R(5,7), and S(8,2).
Describe a sequence of transformations that would map rABC onto rQRS.
B
S
Q
R
A
C
y
x
Score 0: The student wrote an incomplete description of a sequence of transformations.
Geometry – Jan. ’19 [26]
Question 29
29 Given points A, B, and C, use a compass and straightedge to construct point D so that ABCD is
a parallelogram.
[Leave all construction marks.]
A
B
C
Score 2: The student gave a complete and correct response.
Geometry – Jan. ’19 [27]
Question 29
29 Given points A, B, and C, use a compass and straightedge to construct point D so that ABCD is
a parallelogram.
[Leave all construction marks.]
A
B
C
Score 2: The student gave a complete and correct response.
Geometry – Jan. ’19 [28]
Question 29
29 Given points A, B, and C, use a compass and straightedge to construct point D so that ABCD is
a parallelogram.
[Leave all construction marks.]
A
B
C
Score 2: The student gave a complete and correct response.
Geometry – Jan. ’19 [29]
Question 29
29 Given points A, B, and C, use a compass and straightedge to construct point D so that ABCD is
a parallelogram.
[Leave all construction marks.]
A
B
C
Score 2: The student gave a complete and correct response.
Geometry – Jan. ’19 [30]
Question 29
29 Given points A, B, and C, use a compass and straightedge to construct point D so that ABCD is
a parallelogram.
[Leave all construction marks.]
Score 1: The student constructed parallelogram ADBC instead of parallelogram ABCD.
Geometry – Jan. ’19 [31]
Question 29
29 Given points A, B, and C, use a compass and straightedge to construct point D so that ABCD is
a parallelogram.
[Leave all construction marks.]
A
B
C
Score 0: The student made an error by constructing ADBC and made an incorrect assumption
that m∠C 90°.
Geometry – Jan. ’19 [32]
Question 30
Score 2: The student gave a complete and correct response.
30 On the set of axes below, rDEF has vertices at the coordinates D(1,1), E(3,4), and F(4,2), and
point G has coordinates (3,1). Owen claims the median from point E must pass through point G.
Is Owen correct? Explain why.
E
F
G
D
y
x
Geometry – Jan. ’19 [33]
Question 30
Score 2: The student gave a complete and correct response.
30 On the set of axes below, rDEF has vertices at the coordinates D(1,1), E(3,4), and F(4,2), and
point G has coordinates (3,1). Owen claims the median from point E must pass through point G.
Is Owen correct? Explain why.
E
F
G
D
y
x
Geometry – Jan. ’19 [34]
Question 30
Score 2: The student gave a complete and correct response. The student supported their claim
graphically that G is not the midpoint.
30 On the set of axes below, rDEF has vertices at the coordinates D(1,1), E(3,4), and F(4,2), and
point G has coordinates (3,1). Owen claims the median from point E must pass through point G.
Is Owen correct? Explain why.
E
F
G
D
y
x
Geometry – Jan. ’19 [35]
Question 30
Score 1: The student did not support their claim that point G is not the midpoint.
30 On the set of axes below, rDEF has vertices at the coordinates D(1,1), E(3,4), and F(4,2), and
point G has coordinates (3,1). Owen claims the median from point E must pass through point G.
Is Owen correct? Explain why.
E
F
G
D
y
x
Geometry – Jan. ’19 [36]
Question 30
Score 0: The student did not show enough correct relevant work to receive any credit.
30 On the set of axes below, rDEF has vertices at the coordinates D(1,1), E(3,4), and F(4,2), and
point G has coordinates (3,1). Owen claims the median from point E must pass through point G.
Is Owen correct? Explain why.
E
F
G
D
y
x
Geometry – Jan. ’19 [37]
Question 31
31 A walking path at a local park is modeled on the grid below where the length of each grid square
is 10 feet. The town needs to submit paperwork to pave the walking path. Determine and state,
to the nearest square foot, the area of the walking path.
50
80
60
40
20
0
100 1500
Score 2: The student gave a complete and correct response.
Geometry – Jan. ’19 [38]
Question 31
31 A walking path at a local park is modeled on the grid below where the length of each grid square
is 10 feet. The town needs to submit paperwork to pave the walking path. Determine and state,
to the nearest square foot, the area of the walking path.
50
80
60
40
20
0
100 1500
Score 1: The student made a scale error in determining the radii of the two concentric circles.
Geometry – Jan. ’19 [39]
Question 31
31 A walking path at a local park is modeled on the grid below where the length of each grid square
is 10 feet. The town needs to submit paperwork to pave the walking path. Determine and state,
to the nearest square foot, the area of the walking path.
50
80
60
40
20
0
100 1500
Score 1: The student rounded incorrectly by using π 3.14, which resulted in an incorrect
final answer.
Geometry – Jan. ’19 [40]
Question 31
31 A walking path at a local park is modeled on the grid below where the length of each grid square
is 10 feet. The town needs to submit paperwork to pave the walking path. Determine and state,
to the nearest square foot, the area of the walking path.
50
80
60
40
20
0
100 1500
Score 1: The student found the correct areas of the two concentric circles.
Geometry – Jan. ’19 [41]
Question 31
31 A walking path at a local park is modeled on the grid below where the length of each grid square
is 10 feet. The town needs to submit paperwork to pave the walking path. Determine and state,
to the nearest square foot, the area of the walking path.
50
80
60
40
20
0
100 1500
Score 1: The student found the correct areas of two concentric semicircles.
Geometry – Jan. ’19 [42]
Question 31
31 A walking path at a local park is modeled on the grid below where the length of each grid square
is 10 feet. The town needs to submit paperwork to pave the walking path. Determine and state,
to the nearest square foot, the area of the walking path.
50
80
60
40
20
0
100 1500
Score 1: The student found appropriate areas of the two concentric circles.
Geometry – Jan. ’19 [43]
Question 31
31 A walking path at a local park is modeled on the grid below where the length of each grid square
is 10 feet. The town needs to submit paperwork to pave the walking path. Determine and state,
to the nearest square foot, the area of the walking path.
50
80
60
40
20
0
100 1500
Score 0: The student did not show enough correct relevant work to receive any credit.
Geometry – Jan. ’19 [44]
Question 31
31 A walking path at a local park is modeled on the grid below where the length of each grid square
is 10 feet. The town needs to submit paperwork to pave the walking path. Determine and state,
to the nearest square foot, the area of the walking path.
50
80
60
40
20
0
100 1500
Score 0: The student did not show enough correct relevant work to receive any credit.
Geometry – Jan. ’19 [45]
Question 32
Score 4: The student gave a complete and correct response.
32 A triangle has vertices A(2,4), B(6,2), and C(1,1).
Prove that rABC is an isosceles right triangle.
[The use of the set of axes below is optional.]
y
x
Geometry – Jan. ’19 [46]
Question 32
Score 4: The student gave a complete and correct response.
32 A triangle has vertices A(2,4), B(6,2), and C(1,1).
Prove that rABC is an isosceles right triangle.
[The use of the set of axes below is optional.]
y
x
Geometry – Jan. ’19 [47]
Question 32
Score 3: The student wrote an incomplete conclusion when proving rA BC is a right triangle.
The student’s proof does not rely on the graph, therefore the graphing error is not
penalized.
32 A triangle has vertices A(2,4), B(6,2), and C(1,1).
Prove that rABC is an isosceles right triangle.
[The use of the set of axes below is optional.]
y
x
Geometry – Jan. ’19 [48]
Question 32
Score 2: The student correctly proved rABC is isosceles, but no further correct work was shown.
32 A triangle has vertices A(2,4), B(6,2), and C(1,1).
Prove that rABC is an isosceles right triangle.
[The use of the set of axes below is optional.]
y
x
Geometry – Jan. ’19 [49]
Question 32
Score 2: The student correctly proved rA BC is a right triangle, but no further correct work was
shown.
32 A triangle has vertices A(2,4), B(6,2), and C(1,1).
Prove that rABC is an isosceles right triangle.
[The use of the set of axes below is optional.]
y
x
Geometry – Jan. ’19 [50]
Question 32
Score 2: The student wrote one incomplete conclusion and one incorrect conclusion.
32 A triangle has vertices A(2,4), B(6,2), and C(1,1).
Prove that rABC is an isosceles right triangle.
[The use of the set of axes below is optional.]
y
x
Geometry – Jan. ’19 [51]
Question 32
Score 1: The student wrote an incomplete conclusion when proving rA BC is isosceles. No
further correct work was shown.
32 A triangle has vertices A(2,4), B(6,2), and C(1,1).
Prove that rABC is an isosceles right triangle.
[The use of the set of axes below is optional.]
y
x
Geometry – Jan. ’19 [52]
Question 32
Score 1: The student used a Pythagorean Triple incorrectly, but made an appropriate conclusion.
No further correct work was shown.
32 A triangle has vertices A(2,4), B(6,2), and C(1,1).
Prove that rABC is an isosceles right triangle.
[The use of the set of axes below is optional.]
y
x
Geometry – Jan. ’19 [53]
Question 32
Score 0: The student did not show enough correct relevant work to receive any credit.
32 A triangle has vertices A(2,4), B(6,2), and C(1,1).
Prove that rABC is an isosceles right triangle.
[The use of the set of axes below is optional.]
y
x
Geometry – Jan. ’19 [54]
Question 33
33 Theresa has a rectangular pool 30 ft long, 15 ft wide, and 4 ft deep. Theresa fills her pool using
city water at a rate of $3.95 per 100 gallons of water.
Nancy has a circular pool with a diameter of 24 ft and a depth of 4 ft. Nancy fills her pool with a
water delivery service at a rate of $200 per 6000 gallons.
If Theresa and Nancy both fill their pools 6 inches from the top of the pool, determine and state
who paid more to fill her pool. [1 ft
3
water 7.48 gallons]
Score 4: The student gave a complete and correct response.
Geometry – Jan. ’19 [55]
Question 33
33 Theresa has a rectangular pool 30 ft long, 15 ft wide, and 4 ft deep. Theresa fills her pool using
city water at a rate of $3.95 per 100 gallons of water.
Nancy has a circular pool with a diameter of 24 ft and a depth of 4 ft. Nancy fills her pool with a
water delivery service at a rate of $200 per 6000 gallons.
If Theresa and Nancy both fill their pools 6 inches from the top of the pool, determine and state
who paid more to fill her pool. [1 ft
3
water 7.48 gallons]
Score 3: The student used 24, the diameter, as the radius of Nancy’s pool.
Geometry – Jan. ’19 [56]
Question 33
33 Theresa has a rectangular pool 30 ft long, 15 ft wide, and 4 ft deep. Theresa fills her pool using
city water at a rate of $3.95 per 100 gallons of water.
Nancy has a circular pool with a diameter of 24 ft and a depth of 4 ft. Nancy fills her pool with a
water delivery service at a rate of $200 per 6000 gallons.
If Theresa and Nancy both fill their pools 6 inches from the top of the pool, determine and state
who paid more to fill her pool. [1 ft
3
water 7.48 gallons]
Score 2: The student made an error in using 4 feet for the depth. The student made a tran-
scription error by using 7.84 when converting to gallons.
Geometry – Jan. ’19 [57]
Question 33
33 Theresa has a rectangular pool 30 ft long, 15 ft wide, and 4 ft deep. Theresa fills her pool using
city water at a rate of $3.95 per 100 gallons of water.
Nancy has a circular pool with a diameter of 24 ft and a depth of 4 ft. Nancy fills her pool with a
water delivery service at a rate of $200 per 6000 gallons.
If Theresa and Nancy both fill their pools 6 inches from the top of the pool, determine and state
who paid more to fill her pool. [1 ft
3
water 7.48 gallons]
Score 1: The student found both volumes using 4 feet for the depth.
Geometry – Jan. ’19 [58]
Question 33
33 Theresa has a rectangular pool 30 ft long, 15 ft wide, and 4 ft deep. Theresa fills her pool using
city water at a rate of $3.95 per 100 gallons of water.
Nancy has a circular pool with a diameter of 24 ft and a depth of 4 ft. Nancy fills her pool with a
water delivery service at a rate of $200 per 6000 gallons.
If Theresa and Nancy both fill their pools 6 inches from the top of the pool, determine and state
who paid more to fill her pool. [1 ft
3
water 7.48 gallons]
Score 1: The student made a conceptual error using the volume of a cone for the volume of the
cylinder. The student made a computational error using 4 feet for the depth.
Geometry – Jan. ’19 [59]
Question 33
33 Theresa has a rectangular pool 30 ft long, 15 ft wide, and 4 ft deep. Theresa fills her pool using
city water at a rate of $3.95 per 100 gallons of water.
Nancy has a circular pool with a diameter of 24 ft and a depth of 4 ft. Nancy fills her pool with a
water delivery service at a rate of $200 per 6000 gallons.
If Theresa and Nancy both fill their pools 6 inches from the top of the pool, determine and state
who paid more to fill her pool. [1 ft
3
water 7.48 gallons]
Score 1: The student found the correct volume of water in one pool, but no further correct work
was shown.
Geometry – Jan. ’19 [60]
Question 33
33 Theresa has a rectangular pool 30 ft long, 15 ft wide, and 4 ft deep. Theresa fills her pool using
city water at a rate of $3.95 per 100 gallons of water.
Nancy has a circular pool with a diameter of 24 ft and a depth of 4 ft. Nancy fills her pool with a
water delivery service at a rate of $200 per 6000 gallons.
If Theresa and Nancy both fill their pools 6 inches from the top of the pool, determine and state
who paid more to fill her pool. [1 ft
3
water 7.48 gallons]
Score 0: The student did not show enough correct relevant work to receive any credit.
Geometry – Jan. ’19 [61]
Question 33
33 Theresa has a rectangular pool 30 ft long, 15 ft wide, and 4 ft deep. Theresa fills her pool using
city water at a rate of $3.95 per 100 gallons of water.
Nancy has a circular pool with a diameter of 24 ft and a depth of 4 ft. Nancy fills her pool with a
water delivery service at a rate of $200 per 6000 gallons.
If Theresa and Nancy both fill their pools 6 inches from the top of the pool, determine and state
who paid more to fill her pool. [1 ft
3
water 7.48 gallons]
Score 0: The student gave a completely incorrect response.
Geometry – Jan. ’19 [62]
Question 34
34 As modeled in the diagram below, an access ramp starts on flat ground and ends at the beginning
of the top step. Each step is 6 inches tall and 8 inches deep.
If the angle of elevation of the ramp is 4.76°, determine and state the length of the ramp, to the
nearest tenth of a foot.
6 in
8 in
6 in
8 in
8 in
Ramp
6 in
d
Score 4: The student gave a complete and correct response.
Determine and state, to the nearest tenth of a foot, the horizontal distance, d, from the bottom of
the stairs to the bottom of the ramp.
Geometry – Jan. ’19 [63]
Question 34
34 As modeled in the diagram below, an access ramp starts on flat ground and ends at the beginning
of the top step. Each step is 6 inches tall and 8 inches deep.
If the angle of elevation of the ramp is 4.76°, determine and state the length of the ramp, to the
nearest tenth of a foot.
6 in
8 in
6 in
8 in
8 in
Ramp
6 in
d
Score 4: The student gave a complete and correct response.
Determine and state, to the nearest tenth of a foot, the horizontal distance, d, from the bottom of
the stairs to the bottom of the ramp.
Geometry – Jan. ’19 [64]
Question 34
34 As modeled in the diagram below, an access ramp starts on flat ground and ends at the beginning
of the top step. Each step is 6 inches tall and 8 inches deep.
If the angle of elevation of the ramp is 4.76°, determine and state the length of the ramp, to the
nearest tenth of a foot.
6 in
8 in
6 in
8 in
8 in
Ramp
6 in
d
Score 3: The student incorrectly subtracted 2 feet in determining the horizontal distance.
Determine and state, to the nearest tenth of a foot, the horizontal distance, d, from the bottom of
the stairs to the bottom of the ramp.
Geometry – Jan. ’19 [65]
Question 34
34 As modeled in the diagram below, an access ramp starts on flat ground and ends at the beginning
of the top step. Each step is 6 inches tall and 8 inches deep.
If the angle of elevation of the ramp is 4.76°, determine and state the length of the ramp, to the
nearest tenth of a foot.
6 in
8 in
6 in
8 in
8 in
Ramp
6 in
d
Score 3: The student did not subtract 16 inches when determining the horizontal distance.
Determine and state, to the nearest tenth of a foot, the horizontal distance, d, from the bottom of
the stairs to the bottom of the ramp.
Geometry – Jan. ’19 [66]
Question 34
34 As modeled in the diagram below, an access ramp starts on flat ground and ends at the beginning
of the top step. Each step is 6 inches tall and 8 inches deep.
If the angle of elevation of the ramp is 4.76°, determine and state the length of the ramp, to the
nearest tenth of a foot.
6 in
8 in
6 in
8 in
8 in
Ramp
6 in
d
Score 2: The student found the correct length of the ramp, but no further correct work was
shown.
Determine and state, to the nearest tenth of a foot, the horizontal distance, d, from the bottom of
the stairs to the bottom of the ramp.
Geometry – Jan. ’19 [67]
Question 34
34 As modeled in the diagram below, an access ramp starts on flat ground and ends at the beginning
of the top step. Each step is 6 inches tall and 8 inches deep.
If the angle of elevation of the ramp is 4.76°, determine and state the length of the ramp, to the
nearest tenth of a foot.
6 in
8 in
6 in
8 in
8 in
Ramp
6 in
d
Score 2: The student used an incorrect trigonometric equation when determining the length of
the ramp. The student incorrectly subtracted 12 inches when determining the
horizontal distance.
Determine and state, to the nearest tenth of a foot, the horizontal distance, d, from the bottom of
the stairs to the bottom of the ramp.
Geometry – Jan. ’19 [68]
Question 34
34 As modeled in the diagram below, an access ramp starts on flat ground and ends at the beginning
of the top step. Each step is 6 inches tall and 8 inches deep.
If the angle of elevation of the ramp is 4.76°, determine and state the length of the ramp, to the
nearest tenth of a foot.
6 in
8 in
6 in
8 in
8 in
Ramp
6 in
d
Score 1: The student wrote one correct trigonometric equation, but no further correct work was
shown.
Determine and state, to the nearest tenth of a foot, the horizontal distance, d, from the bottom of
the stairs to the bottom of the ramp.
Geometry – Jan. ’19 [69]
Question 34
34 As modeled in the diagram below, an access ramp starts on flat ground and ends at the beginning
of the top step. Each step is 6 inches tall and 8 inches deep.
If the angle of elevation of the ramp is 4.76°, determine and state the length of the ramp, to the
nearest tenth of a foot.
6 in
8 in
6 in
8 in
8 in
Ramp
6 in
d
Score 0: The student gave a completely incorrect response.
Determine and state, to the nearest tenth of a foot, the horizontal distance, d, from the bottom of
the stairs to the bottom of the ramp.
Geometry – Jan. ’19 [70]
Question 35
35 In the diagram of quadrilateral ABCD with diagonal shown below, segments GH and EF are
drawn, 艑 , 艑 , 艑 , and 艑 .
Prove: 艑
EF G
H
AEB
DCG
H
F
AE CG BE DG AH CF AD CB
AC
Score 6: The student gave a complete and correct response.
Work space for question 35 is continued on the next page.
Geometry – Jan. ’19 [71]
Question 35
35 In the diagram of quadrilateral ABCD with diagonal shown below, segments GH and EF are
drawn, 艑 , 艑 , 艑 , and 艑 .
Prove: 艑
EF G
H
AEB
DCG
H
F
AE CG BE DG AH CF AD CB
AC
Score 6: The student gave a complete and correct response.
Work space for question 35 is continued on the next page.
Geometry – Jan. ’19 [72]
Question 35
35 In the diagram of quadrilateral ABCD with diagonal shown below, segments GH and EF are
drawn, 艑 , 艑 , 艑 , and 艑 .
Prove: 艑
EF G
H
AEB
DCG
H
F
AE CG BE DG AH CF AD CB
AC
Score 6: The student gave a complete and correct response.
Work space for question 35 is continued on the next page.
Geometry – Jan. ’19 [73]
Question 35
Question 35 continued
Geometry – Jan. ’19 [74]
Question 35
35 In the diagram of quadrilateral ABCD with diagonal shown below, segments GH and EF are
drawn, 艑 , 艑 , 艑 , and 艑 .
Prove: 艑
EF G
H
AEB
DCG
H
F
AE CG BE DG AH CF AD CB
AC
Score 5: The student had an incomplete reason in step 6.
Work space for question 35 is continued on the next page.
Geometry – Jan. ’19 [75]
Question 35
35 In the diagram of quadrilateral ABCD with diagonal shown below, segments GH and EF are
drawn, 艑 , 艑 , 艑 , and 艑 .
Prove: 艑
EF G
H
AEB
DCG
H
F
AE CG BE DG AH CF AD CB
AC
Score 4: The student made a conceptual error by claiming parallel sides came from
the quadrilateral in step 5.
Work space for question 35 is continued on the next page.
Geometry – Jan. ’19 [76]
Question 35
35 In the diagram of quadrilateral ABCD with diagonal shown below, segments GH and EF are
drawn, 艑 , 艑 , 艑 , and 艑 .
Prove: 艑
EF G
H
AEB
DCG
H
F
AE CG BE DG AH CF AD CB
AC
Score 4: The student stated the wrong parallel sides in step 6, followed by an incorrect reason
in step 7.
Work space for question 35 is continued on the next page.
Geometry – Jan. ’19 [77]
Question 35
35 In the diagram of quadrilateral ABCD with diagonal shown below, segments GH and EF are
drawn, 艑 , 艑 , 艑 , and 艑 .
Prove: 艑
EF G
H
AEB
DCG
H
F
AE CG BE DG AH CF AD CB
AC
Score 3: The student made a conceptual error by assuming || in step 7 and wrote an
incorrect statement in step 8 based on the wrong parallel sides.
GH
EF
Work space for question 35 is continued on the next page.
Geometry – Jan. ’19 [78]
Question 35
35 In the diagram of quadrilateral ABCD with diagonal shown below, segments GH and EF are
drawn, 艑 , 艑 , 艑 , and 艑 .
Prove: 艑
EF G
H
AEB
DCG
H
F
AE CG BE DG AH CF AD CB
AC
Score 2: The student combined two different approaches by proving ABCD is a parallelogram
and rADC ⬵ r BCA, but no further relevant work was shown.
Work space for question 35 is continued on the next page.
Geometry – Jan. ’19 [79]
Question 35
35 In the diagram of quadrilateral ABCD with diagonal shown below, segments GH and EF are
drawn, 艑 , 艑 , 艑 , and 艑 .
Prove: 艑
EF G
H
AEB
DCG
H
F
AE CG BE DG AH CF AD CB
AC
Score 2: The student proved rACD ⬵ rCAB, but no further correct work was shown.
Work space for question 35 is continued on the next page.
Geometry – Jan. ’19 [80]
Question 35
35 In the diagram of quadrilateral ABCD with diagonal shown below, segments GH and EF are
drawn, 艑 , 艑 , 艑 , and 艑 .
Prove: 艑
EF G
H
AEB
DCG
H
F
AE CG BE DG AH CF AD CB
AC
Score 1: The student had one correct relevant statement and reason.
Work space for question 35 is continued on the next page.
Geometry – Jan. ’19 [81]
Question 35
35 In the diagram of quadrilateral ABCD with diagonal shown below, segments GH and EF are
drawn, 艑 , 艑 , 艑 , and 艑 .
Prove: 艑
EF G
H
AEB
DCG
H
F
AE CG BE DG AH CF AD CB
AC
Score 0: The student did not show enough correct relevant work to receive any credit.
Work space for question 35 is continued on the next page.
