# Determine whether the polygons are similar - Expert Answer

Question 1: Determine whether the polygons are similar. If so, identify the correct similarity ratio and the similarity statement.

Determine whether the polygons are similar. If so, identify the correct similarity ratio and the similarity statement.

Question 2: Determine whether the two triangles are similar

Determine whether the two triangles are similar.

ΔKLJ ~ ΔRPQ by SSS~

The triangles are not necessarily similar.

ΔKLJ ~ ΔRPQ by SAS~

ΔKLJ ~ ΔRPQ by AA~

Question 3: Identify the correct explanation for why the triangles are similar. Then find <emSQ</em and

Identify the correct explanation for why the triangles are similar. Then find SQ and TP.

Question 4: <=""<br<=""

QS = 2, SR = 8

QS = 9.6, SR = 8

QS = 5, SR = 6

QS = 8, SR = 9.6

Question 5: Identify the perimeter and area of

ΔMNO ~ ΔDEF. Identify the perimeter and area of ΔMNO to the nearest tenth.

P ≈ 38.7 in., A ≈ 207.5 in2

P ≈ 69.9 in., A ≈ 207.5 in2

P =≈ 69.9 in., A ≈ 163.7 in2

P ≈ 38.7 in., A ≈ 63.7 in2

Question 6 Identify the coordinates of and the scale factor

ΔAOC ~ ΔBOD. Identify the coordinates of D and the scale factor.

Question 7: what is the length of

If TW = 12 and VW = 8, what is the length of UW?

UW = 12

UW = 4

UW = 8

UW = 18

Question 8: Use a special right triangle to write sin 30° as a fraction.

Use a special right triangle to write sin 30° as a fraction.

Question 9: Find the unknown measures. Round lengths to the nearest hundredth and angle measures to the nearest degree.

Find the unknown measures. Round lengths to the nearest hundredth and angle measures to the nearest degree.

KM ≈ 10.41; m∠K ≈ 53°; m∠M ≈ 33°

KM ≈ 10.68; m∠K ≈ 55°; m∠M ≈ 35°

KM ≈ 10.51; m∠K ≈ 53°; m∠M ≈ 34°

KM ≈ 10.52; m∠K ≈ 54°; m∠M ≈ 34°

Question 10: When observed from the top of a 250-ft-tall lighthouse, the angle of depression of an approaching ship is 50°. Identify the horizontal distance from the lighthouse to the ship rounded to the nearest foot.

When observed from the top of a 250-ft-tall lighthouse, the angle of depression of an approaching ship is 50°. Identify the horizontal distance from the lighthouse to the ship rounded to the nearest foot.

192 ft

298 ft

210 ft

161 ft

Question 11:

In ΔABC, a = 26,b = 19, and c = 17.2. Identify m∠C rounded to the nearest degree.

50°

46°

41°

37°

Question 12: <=""

Question 13: Identify the area of the trapezoid.<br<=""

Identify the area of the trapezoid.

A = 94.5x2 cm2

A = 94.5x cm2

A = 189x cm2

A = 189x2 cm2

Question 14: Identify the area of the rhombus.<br<=""

Identify the area of the rhombus.

A = 1,176 in2

A = 980 in2

A = 2,352 in2

A = 1,960 in2

Question 15: Identify the area of in terms of

Identify the area of ⊙M in terms of π.

A = 196π m2

A = 56π m2

A = 28π m2

A = 14π m2

Question 16: Identify the area of a regular hexagon with side length 14 in. rounded to the nearest tenth.

Identify the area of a regular hexagon with side length 14 in. rounded to the nearest tenth.

A ≈ 509.2 in2

A ≈ 169.7 in2

A ≈ 678.9 in2

A ≈ 1018.4 in2

Question 17: Identify the area of the figure rounded to the nearest tenth

Identify the area of the figure rounded to the nearest tenth.

139.9 cm2

212.4 cm2

199.9 cm2

152.4 cm2

Question 18: Identify the polygon with vertices and then find the perimeter and area of the polygon.

Identify the polygon with vertices A (5, 0), B (2, 4), C (−2, 1), and D (1, −3), and then find the perimeter and area of the polygon.

kite; P = 19 units; A = 21 units2

kite; P = 18.7 units; A = 25 units2

square; P = 20.5 units; A = 24.5 units2

square; P = 20 units; A = 25 units2

Question 19: The height of a rectangle is multiplied by 4. Which of the following describes the effect of this change on the area?</p

The height of a rectangle is multiplied by 4. Which of the following describes the effect of this change on the area?

The area is multiplied by 4.

The area is multiplied by 16.

The area is multiplied by 8.

The area is multiplied by 2.

Question 20: A square has side length of 9 in. If the area is doubled, what happens to the side length?<br

A square has side length of 9 in. If the area is doubled, what happens to the side length?

The side length is multiplied by 4.

The side length is doubled.

Question 21:

6/13

5/13

2/13

7/13

Question 22: <pIdentify the probability to the nearest hundredth that a point chosen randomly inside the rectangle is in the triangle

Identify the probability to the nearest hundredth that a point chosen randomly inside the rectangle is in the triangle.

0.15

0.31

0.69

0.85

Question 23: Classify the figure. Identify its vertices, edges, and bases

Classify the figure. Identify its vertices, edges, and bases.

Question 24: <pWhich of the following shows all of the six orthographic views of the objects? Assume there are no hidden cubes

Which of the following shows all of the six orthographic views of the objects? Assume there are no hidden cubes.

Question 25: Identify the number of vertices, edges, and faces of the polyhedron. Use your results to verify Euler's formula

Identify the number of vertices, edges, and faces of the polyhedron. Use your results to verify Euler's formula.

V = 4, E = 9, F = 7; 4 − 9 + 7 = 2

V = 6, E = 7, F = 3; 6 − 7 + 3 = 2

V = 4, E = 7, F = 5; 4 − 7 + 5 = 2

V = 6, E = 9, F = 5; 6 − 9 + 5 = 2

Question 26: Identify the surface area of the composite figure to the nearest tenth.<br<=""

Identify the surface area of the composite figure to the nearest tenth.

175.1 m2

212.8 m2

200.2 m2

187.7 m2

Question 27: Identify the surface area of the composite figure in terms of

Identify the surface area of the composite figure in terms of π.

S = 63π m2

S = 48π m2

S = 96π m2

S = 78π m2

Question 28: Identify the volume of the composite figure. Round to the nearest tenth

Identify the volume of the composite figure. Round to the nearest tenth.

192 m3

224 m3

352 m3

384 m3

Question 29: Identify the volume of the composite figure, rounded to the nearest tenth.

Identify the volume of the composite figure, rounded to the nearest tenth.

312 ft3

504 ft3

360 ft3

120 ft3

Question 30: Identify the volume and surface area of a sphere with great circle area Give your answer in terms of

Identify the volume and surface area of a sphere with great circle area 9π m2. Give your answer in terms of π.

V = 36π m3; S = 18π m2

V = 36π m3; S = 36π m2

V = 108π m3; S = 36π m2

V = 18π m3; S = 18π m2

Question 31: <pFind the volume and surface area of the composite figure. Give your answer in terms of

Find the volume and surface area of the composite figure. Give your answer in terms of π.

V = 45π in3; S = 72π in2

V = 99π in3; S = 81π in2

V = 117π in3; S = 90π in2

V = 63π in3; S = 81π in2

Question 32: <pIdentify each line or segment that intersects ⊙

Identify each line or segment that intersects ⊙ T.

Question 33: The circle graph shows the break down of the age group of people living in a city. Identify the measure of arc

The circle graph shows the break down of the age group of people living in a city. Identify the measure of arc QR.

72°

28.8°

45°

288°

Question 34: Identify <emPQ</em rounded to the nearest tenth.<br<=""</p

⊙M ≅ ⊙N and AB = 31.8. Identify PQ rounded to the nearest tenth.

13.8

8.9

18.0

9.6

Question 35: Identify the area of segment to the nearest hundredth.

Identify the area of segment AOB to the nearest hundredth.

≈ 12.56 in2

≈ 6.28 in2

≈ 18.84 in2

≈ 3.26 in2

Question 36: Identify

Identify m∠MNQ.

m∠MNQ = 60°

m∠MNQ = 40°

m∠MNQ = 50°

m∠MNQ = 80°

Question 37: Identify

Identify y.

y = 2

y = 5

y = 3

y = 4

Question 38: Identify

Identify m∠AMB.

m∠AMB = 165°

m∠AMB = 85°

m∠AMB = 82.5°

m∠AMB = 80°

Question 39: Identify the measure of arc

Identify the measure of arc RT.

RT = 35°

RT = 45°

RT = 85°

RT = 40°

Question 40: Identify the value of and the length of each chord.

Identify the value of y and the length of each chord.

y = 5; PQ = 13; RS = 14

y = 5; PQ = 14; RS = 13

y = 10; PQ = 19; RS = 18

y = 10; PQ = 18; RS = 19

Question 41: Identify the value of

Identify the value of x.

x = 16

x = 2

x = 32

x = 4

Question 42: Identify the equation of the circle that passes through and has center

Identify the equation of the circle Y that passes through (2, 6) and has center (3, 4).

(x − 3)2 + ( y − 4)2 = 25

(x + 3)2 + ( y + 4)2 = 25

(x − 3)2 + ( y − 4)2 = 5

(x + 3)2 + ( y + 4)2 = 5

Question 43: Identify the graph of the equation

Identify the graph of the equation (x + 2)2 + ( y − 5)2 = 4.

Question 44: <pIdentify the reflection of the figure with (−12, −36), and

Identify the reflection of the figure with vertices L (−5, 15), M (−12, −36), and N (21, −11) across the y-axis.

L (−5, −15), M (12, 36), N (−21, −11)

L (5, 15), M (12, −36), N (−21, −11)

L (−5, −15), M (−12, 36), N (21, 11)

L (15, −5), M (−36, −12), N (−11, 21)

Question 45: <pIdentify the translation of the figure with vertices (5, −3),

Identify the translation of the figure with vertices W (2, −3), X (5, −3), Y (5, −5), and Z (2, −5) along the vector (−6, 7).

W ′(−4, 4), X ′(−1, 4), Y ′(−1, 2), Z ′(−4, 2)

W ′(4, 0), X ′(−1, 4), Y ′(−1, 2), Z ′(−4, 0)

W ′(4, −4), X ′(−1, 4), Y ′(2, −1), Z ′(−4, 2)

W ′(−4, 4), X ′(−4, 1), Y ′(−1, 2), Z ′(−1, −4)

Question 46: <pWhich of the following represents a rotation, which has vertices (5, −5), about the origin by 90°?</p

Which of the following represents a rotation of ΔLMN, which has vertices L (−7, 7), M (9, 9), andN (5, −5), about the origin by 90°?

L (−7, −7)

M (−9, 9)

N (5, 5)

L (−7, −7)

M (−9, 9)

N (5, −5)

L (−7, −7)

M (−9, −9)

N (5, 5)

L (7, −7)

M (9, 9)

N (−5, 5)

Question 47: Which of the following represents the translation axis?

Which of the following represents the translation of M (8, −2) along the vector (−5, 1) and its reflection across the y-axis?

M (8, −2) → M ′(−40, −2) → M ″(−2, −40)

M (8, −2) → M ′(3, −1) → M ″(−3, 1)

M (8, −2) → M ′(3, −1) → M ″(−3, −1)

M (8, −2) → M ′(3, −1) → M ″(1, −3)

Question 48: <pIdentify whether the figure has plane symmetry, symmetry about an axis, or neither.

Identify whether the figure has plane symmetry, symmetry about an axis, or neither.

plane symmetry

neither plane symmetry nor symmetry about an axis

plane symmetry and symmetry about an axis

symmetry about an axis

Question 49: Identify the tessellation created using the given regular polygons.

Identify the tessellation created using the given regular polygons.

Question 50: Identify the image of the triangle with) under a dilation with a scale factor of −4 centered at the origin.

Identify the image of the triangle with vertices I(−1, −3), J(1, 2), and K(−2, 3) under a dilation with a scale factor of −4 centered at the origin.

Determine whether the polygons are similar. If so, identify the correct similarity ratio and the similarity statement.

Question 2: Determine whether the two triangles are similar

Determine whether the two triangles are similar.

ΔKLJ ~ ΔRPQ by SSS~

The triangles are not necessarily similar.

ΔKLJ ~ ΔRPQ by SAS~

ΔKLJ ~ ΔRPQ by AA~

Question 3: Identify the correct explanation for why the triangles are similar. Then find <emSQ</em and

Identify the correct explanation for why the triangles are similar. Then find SQ and TP.

Question 4: <=""<br<=""

QS = 2, SR = 8

QS = 9.6, SR = 8

QS = 5, SR = 6

QS = 8, SR = 9.6

Question 5: Identify the perimeter and area of

ΔMNO ~ ΔDEF. Identify the perimeter and area of ΔMNO to the nearest tenth.

P ≈ 38.7 in., A ≈ 207.5 in2

P ≈ 69.9 in., A ≈ 207.5 in2

P =≈ 69.9 in., A ≈ 163.7 in2

P ≈ 38.7 in., A ≈ 63.7 in2

Question 6 Identify the coordinates of and the scale factor

ΔAOC ~ ΔBOD. Identify the coordinates of D and the scale factor.

Question 7: what is the length of

If TW = 12 and VW = 8, what is the length of UW?

UW = 12

UW = 4

UW = 8

UW = 18

Question 8: Use a special right triangle to write sin 30° as a fraction.

Use a special right triangle to write sin 30° as a fraction.

Question 9: Find the unknown measures. Round lengths to the nearest hundredth and angle measures to the nearest degree.

Find the unknown measures. Round lengths to the nearest hundredth and angle measures to the nearest degree.

KM ≈ 10.41; m∠K ≈ 53°; m∠M ≈ 33°

KM ≈ 10.68; m∠K ≈ 55°; m∠M ≈ 35°

KM ≈ 10.51; m∠K ≈ 53°; m∠M ≈ 34°

KM ≈ 10.52; m∠K ≈ 54°; m∠M ≈ 34°

Question 10: When observed from the top of a 250-ft-tall lighthouse, the angle of depression of an approaching ship is 50°. Identify the horizontal distance from the lighthouse to the ship rounded to the nearest foot.

When observed from the top of a 250-ft-tall lighthouse, the angle of depression of an approaching ship is 50°. Identify the horizontal distance from the lighthouse to the ship rounded to the nearest foot.

192 ft

298 ft

210 ft

161 ft

Question 11:

In ΔABC, a = 26,b = 19, and c = 17.2. Identify m∠C rounded to the nearest degree.

50°

46°

41°

37°

Question 12: <=""

Question 13: Identify the area of the trapezoid.<br<=""

Identify the area of the trapezoid.

A = 94.5x2 cm2

A = 94.5x cm2

A = 189x cm2

A = 189x2 cm2

Question 14: Identify the area of the rhombus.<br<=""

Identify the area of the rhombus.

A = 1,176 in2

A = 980 in2

A = 2,352 in2

A = 1,960 in2

Question 15: Identify the area of in terms of

Identify the area of ⊙M in terms of π.

A = 196π m2

A = 56π m2

A = 28π m2

A = 14π m2

Question 16: Identify the area of a regular hexagon with side length 14 in. rounded to the nearest tenth.

Identify the area of a regular hexagon with side length 14 in. rounded to the nearest tenth.

A ≈ 509.2 in2

A ≈ 169.7 in2

A ≈ 678.9 in2

A ≈ 1018.4 in2

Question 17: Identify the area of the figure rounded to the nearest tenth

Identify the area of the figure rounded to the nearest tenth.

139.9 cm2

212.4 cm2

199.9 cm2

152.4 cm2

Question 18: Identify the polygon with vertices and then find the perimeter and area of the polygon.

Identify the polygon with vertices A (5, 0), B (2, 4), C (−2, 1), and D (1, −3), and then find the perimeter and area of the polygon.

kite; P = 19 units; A = 21 units2

kite; P = 18.7 units; A = 25 units2

square; P = 20.5 units; A = 24.5 units2

square; P = 20 units; A = 25 units2

Question 19: The height of a rectangle is multiplied by 4. Which of the following describes the effect of this change on the area?</p

The height of a rectangle is multiplied by 4. Which of the following describes the effect of this change on the area?

The area is multiplied by 4.

The area is multiplied by 16.

The area is multiplied by 8.

The area is multiplied by 2.

Question 20: A square has side length of 9 in. If the area is doubled, what happens to the side length?<br

A square has side length of 9 in. If the area is doubled, what happens to the side length?

The side length is multiplied by 4.

The side length is doubled.

Question 21:

6/13

5/13

2/13

7/13

Question 22: <pIdentify the probability to the nearest hundredth that a point chosen randomly inside the rectangle is in the triangle

Identify the probability to the nearest hundredth that a point chosen randomly inside the rectangle is in the triangle.

0.15

0.31

0.69

0.85

Question 23: Classify the figure. Identify its vertices, edges, and bases

Classify the figure. Identify its vertices, edges, and bases.

Question 24: <pWhich of the following shows all of the six orthographic views of the objects? Assume there are no hidden cubes

Which of the following shows all of the six orthographic views of the objects? Assume there are no hidden cubes.

Question 25: Identify the number of vertices, edges, and faces of the polyhedron. Use your results to verify Euler's formula

Identify the number of vertices, edges, and faces of the polyhedron. Use your results to verify Euler's formula.

V = 4, E = 9, F = 7; 4 − 9 + 7 = 2

V = 6, E = 7, F = 3; 6 − 7 + 3 = 2

V = 4, E = 7, F = 5; 4 − 7 + 5 = 2

V = 6, E = 9, F = 5; 6 − 9 + 5 = 2

Question 26: Identify the surface area of the composite figure to the nearest tenth.<br<=""

Identify the surface area of the composite figure to the nearest tenth.

175.1 m2

212.8 m2

200.2 m2

187.7 m2

Question 27: Identify the surface area of the composite figure in terms of

Identify the surface area of the composite figure in terms of π.

S = 63π m2

S = 48π m2

S = 96π m2

S = 78π m2

Question 28: Identify the volume of the composite figure. Round to the nearest tenth

Identify the volume of the composite figure. Round to the nearest tenth.

192 m3

224 m3

352 m3

384 m3

Question 29: Identify the volume of the composite figure, rounded to the nearest tenth.

Identify the volume of the composite figure, rounded to the nearest tenth.

312 ft3

504 ft3

360 ft3

120 ft3

Question 30: Identify the volume and surface area of a sphere with great circle area Give your answer in terms of

Identify the volume and surface area of a sphere with great circle area 9π m2. Give your answer in terms of π.

V = 36π m3; S = 18π m2

V = 36π m3; S = 36π m2

V = 108π m3; S = 36π m2

V = 18π m3; S = 18π m2

Question 31: <pFind the volume and surface area of the composite figure. Give your answer in terms of

Find the volume and surface area of the composite figure. Give your answer in terms of π.

V = 45π in3; S = 72π in2

V = 99π in3; S = 81π in2

V = 117π in3; S = 90π in2

V = 63π in3; S = 81π in2

Question 32: <pIdentify each line or segment that intersects ⊙

Identify each line or segment that intersects ⊙ T.

Question 33: The circle graph shows the break down of the age group of people living in a city. Identify the measure of arc

The circle graph shows the break down of the age group of people living in a city. Identify the measure of arc QR.

72°

28.8°

45°

288°

Question 34: Identify <emPQ</em rounded to the nearest tenth.<br<=""</p

⊙M ≅ ⊙N and AB = 31.8. Identify PQ rounded to the nearest tenth.

13.8

8.9

18.0

9.6

Question 35: Identify the area of segment to the nearest hundredth.

Identify the area of segment AOB to the nearest hundredth.

≈ 12.56 in2

≈ 6.28 in2

≈ 18.84 in2

≈ 3.26 in2

Question 36: Identify

Identify m∠MNQ.

m∠MNQ = 60°

m∠MNQ = 40°

m∠MNQ = 50°

m∠MNQ = 80°

Question 37: Identify

Identify y.

y = 2

y = 5

y = 3

y = 4

Question 38: Identify

Identify m∠AMB.

m∠AMB = 165°

m∠AMB = 85°

m∠AMB = 82.5°

m∠AMB = 80°

Question 39: Identify the measure of arc

Identify the measure of arc RT.

RT = 35°

RT = 45°

RT = 85°

RT = 40°

Question 40: Identify the value of and the length of each chord.

Identify the value of y and the length of each chord.

y = 5; PQ = 13; RS = 14

y = 5; PQ = 14; RS = 13

y = 10; PQ = 19; RS = 18

y = 10; PQ = 18; RS = 19

Question 41: Identify the value of

Identify the value of x.

x = 16

x = 2

x = 32

x = 4

Question 42: Identify the equation of the circle that passes through and has center

Identify the equation of the circle Y that passes through (2, 6) and has center (3, 4).

(x − 3)2 + ( y − 4)2 = 25

(x + 3)2 + ( y + 4)2 = 25

(x − 3)2 + ( y − 4)2 = 5

(x + 3)2 + ( y + 4)2 = 5

Question 43: Identify the graph of the equation

Identify the graph of the equation (x + 2)2 + ( y − 5)2 = 4.

Question 44: <pIdentify the reflection of the figure with (−12, −36), and

Identify the reflection of the figure with vertices L (−5, 15), M (−12, −36), and N (21, −11) across the y-axis.

L (−5, −15), M (12, 36), N (−21, −11)

L (5, 15), M (12, −36), N (−21, −11)

L (−5, −15), M (−12, 36), N (21, 11)

L (15, −5), M (−36, −12), N (−11, 21)

Question 45: <pIdentify the translation of the figure with vertices (5, −3),

Identify the translation of the figure with vertices W (2, −3), X (5, −3), Y (5, −5), and Z (2, −5) along the vector (−6, 7).

W ′(−4, 4), X ′(−1, 4), Y ′(−1, 2), Z ′(−4, 2)

W ′(4, 0), X ′(−1, 4), Y ′(−1, 2), Z ′(−4, 0)

W ′(4, −4), X ′(−1, 4), Y ′(2, −1), Z ′(−4, 2)

W ′(−4, 4), X ′(−4, 1), Y ′(−1, 2), Z ′(−1, −4)

Question 46: <pWhich of the following represents a rotation, which has vertices (5, −5), about the origin by 90°?</p

Which of the following represents a rotation of ΔLMN, which has vertices L (−7, 7), M (9, 9), andN (5, −5), about the origin by 90°?

L (−7, −7)

M (−9, 9)

N (5, 5)

L (−7, −7)

M (−9, 9)

N (5, −5)

L (−7, −7)

M (−9, −9)

N (5, 5)

L (7, −7)

M (9, 9)

N (−5, 5)

Question 47: Which of the following represents the translation axis?

Which of the following represents the translation of M (8, −2) along the vector (−5, 1) and its reflection across the y-axis?

M (8, −2) → M ′(−40, −2) → M ″(−2, −40)

M (8, −2) → M ′(3, −1) → M ″(−3, 1)

M (8, −2) → M ′(3, −1) → M ″(−3, −1)

M (8, −2) → M ′(3, −1) → M ″(1, −3)

Question 48: <pIdentify whether the figure has plane symmetry, symmetry about an axis, or neither.

Identify whether the figure has plane symmetry, symmetry about an axis, or neither.

plane symmetry

neither plane symmetry nor symmetry about an axis

plane symmetry and symmetry about an axis

symmetry about an axis

Question 49: Identify the tessellation created using the given regular polygons.

Identify the tessellation created using the given regular polygons.

Question 50: Identify the image of the triangle with) under a dilation with a scale factor of −4 centered at the origin.

Identify the image of the triangle with vertices I(−1, −3), J(1, 2), and K(−2, 3) under a dilation with a scale factor of −4 centered at the origin.

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