Similar Figures Answers

On a coordinate plane, trapezoids A B D C and M N P Q are shown. The length of A B is 4 units and the length of B D is 2 units. The length of M N is 10 units and the length of N P is 6 units.

A

Yes, because AB and CD are each the lengths MN and QP.

B

Yes, because sides AB and CD are parallel to sides MN and QP.

C

No, because AB is the length MN but CD is the length QP.

D

No, because sides AB and CD have different slopes from sides MN and QP.

2

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What is true about the image ΔQ'R'S'? Select three options.Which statements are true?

A

DO,2 (x,y) = (2x, 2y)

B

Side Q'S' lies on a line with a slope of -1.

C

QR is longer than Q'R'.

D

The vertices of the image are closer to the origin than those of the pre-image.

E

The distance from Q' to the origin is twice the distance from Q to the origin.

3

Which statements are true about the parallelograms? Select three options.

A

The length of side MN is 2 units.

B

The length of side M'N' is 5 units.

C

The image is smaller than the pre-image.

D

Sides MQ and M'Q' both have the same slope, 1.

E

The scale factor is .

4

Which graph shows a dilation?

A

On a coordinate plane, 2 quadrilaterals are shown. The larger quadrilateral has points (negative 4, 3), (0, 3), (2, 0), and (negative 2, 0). The smaller quadrilateral has points (negative 2, 2), (0, 2), (0.5, 0), and (negative 1.5, 0).

B

On a coordinate plane, 2 quadrilaterals are shown. The larger quadrilateral has points (negative 4, 3), (0, 3), (2, 0), and (negative 2, 0). The smaller quadrilateral has points (negative 2, 2), (0, 2), (0.5, 0), and (negative 1.5, 0).

C

On a coordinate plane, 2 quadrilaterals are shown. The larger quadrilateral has points (negative 5, 3), (1, 3), (4, 0), (negative 2, 0). The smaller quadrilateral has points (negative 1, 0), (negative 2, 1), (0, 1), and (1, 0).

D

On a coordinate plane, 2 quadrilaterals are shown. The larger quadrilateral has points (negative 5, 3), (1, 3), (4, 0), (negative 2, 0). The smaller quadrilateral has points (negative 0.5, 0), (negative 1, 2), (1, 2), (1.5, 0).

5

Triangle MNP is dilated according to the rule DO,1.5 (x,y)(1.5x, 1.5y) to create the image triangle M'N'P, which is not shown.

M

M'(-6, 9) and N'(4, 9)

M

M'(-6, 9) and N'(3, 9)

M

M'(-2, 3) and N'(7, 9)

M

M'(-2, 3) and N'(1, 3)

6

On a coordinate plane, 2 polygons are shown. Polygon A B C D is larger than polygon A prime B prime C prime D prime and is reflected across the y-axis to form polygon A prime B prime C prime D prime.

a

a dilation with a scale factor less than 1 and then a reflection

a

a dilation with a scale factor less than 1 and then a translation

a

a dilation with a scale factor greater than 1 and then a reflection

a

a dilation with a scale factor greater than 1 and then a translation

7

Triangle STV was dilated with the origin as the center of dilation to form S'T'V'.

A

Option

B

Option

C

Option

D

Option

8

Which graph shows a dilation?

A

Option

B

Option

C

Option

D

Option

9

Which statements are true? Select three options.

A

∠F corresponds to ∠F'.

B

Segment EE' is parallel to segment FF'.

C

The distance from point D' to the origin is the distance of point D to the origin.

D

The measure of ∠E' is the measure of ∠E.

E

△DEF △D'E'F'

10

Which statements are true about the trapezoids? Select three options.

A

The length of side AD is 8 units.

B

The length of side A'D' is 4 units.

C

The image is larger than the pre-image.

D

Sides CD and C'D' both have the same slope, 2.

E

The scale factor is .

11

Triangle MNP is dilated according to the rule DO,1.5 (x,y)(1.5x, 1.5y) to create the image triangle M'N'P, which is not shown.

A

M'(-6, 9) and N'(4, 9)

B

M'(-6, 9) and N'(3, 9)

C

M'(-2, 3) and N'(7, 9)

D

M'(-2, 3) and N'(1, 3)

12

On a coordinate plane, 2 quadrilaterals are shown. Quadrilateral A B C D has points (2, negative 2), (4, negative 2), (3, negative 4), and (1, negative 4). Quadrilateral J K L M has points (4, negative 4), (8, negative 4), (6, negative 9), and (2, negative 9).

A

Yes, because sides JK and ML are twice as long as sides AB and DC.

B

Yes, because both figures are parallelograms, so corresponding sides are parallel.

C

No, because sides JK and ML are not twice as long as sides AB and DC.

D

No, because sides JM and KL have different slopes from sides AD and BC.

13

On a coordinate plane, 2 polygons are shown. Polygon A B C D is larger than polygon A prime B prime C prime D prime and is reflected across the y-axis to form polygon A prime B prime C prime D prime.

A

a dilation with a scale factor less than 1 and then a reflection

B

a dilation with a scale factor less than 1 and then a translation

C

a dilation with a scale factor greater than 1 and then a reflection

D

a dilation with a scale factor greater than 1 and then a translation

14

Triangle ABC was dilated and translated to form similar triangle A'B'C'.

A

One-fifth

B

Two-fifths

C

Five-halves

D

5

15

What is true about the image ΔQ'R'S'? Select three options.Which statements are true?

A

DO,2 (x,y) = (2x, 2y)

B

Side Q'S' lies on a line with a slope of -1.

C

QR is longer than Q'R'.

D

The vertices of the image are closer to the origin than those of the pre-image.

E

The distance from Q' to the origin is twice the distance from Q to the origin.

16

Which statements are true about the trapezoids? Select three options.

A

The length of side AD is 8 units.

B

The length of side A'D' is 4 units.

C

The image is larger than the pre-image.

D

Sides CD and C'D' both have the same slope, 2.

E

The scale factor is .

17

Which graph shows a dilation?

A

On a coordinate plane, 2 rectangles are shown. The larger rectangle is 8 units wide and 4 units high. The smaller rectangle is 4 units wide and 2 units high.

B

On a coordinate plane, a square and a rectangle are shown. The square is 2 units wide and 2 units high. The rectangle is 8 units wide and 4 units high.

C

On a coordinate plane, 2 rectangles are shown. The larger rectangle is 7 units wide and 4 units high. The smaller rectangle is 3 units wide and 2 units high.

D

On a coordinate plane, 2 rectangles are shown. The larger rectangle is 7 units wide and 4 units high. The smaller rectangle is 3 units wide and 1 unit high.

18

Trapezoid DEFG is dilated according to the ruleDO,4(x,y) to form the image trapezoid D'E'F'G', which is shown on the graph.

A

(-2, 1)

B

(-4, 2)

C

(-12, 0)

D

(-32, 16)

19

Which graph shows a dilation?

A

On a coordinate plane, 2 quadrilaterals are shown. The larger quadrilateral has points (negative 4, 3), (0, 3), (2, 0), and (negative 2, 0). The smaller quadrilateral has points (negative 2, 2), (0, 2), (0.5, 0), and (negative 1.5, 0).

B

On a coordinate plane, 2 quadrilaterals are shown. The larger quadrilateral has points (negative 4, 3), (0, 3), (2, 0), and (negative 2, 0). The smaller quadrilateral has points (negative 2, 2), (0, 2), (0.5, 0), and (negative 1.5, 0).

C

On a coordinate plane, 2 quadrilaterals are shown. The larger quadrilateral has points (negative 5, 3), (1, 3), (4, 0), (negative 2, 0). The smaller quadrilateral has points (negative 1, 0), (negative 2, 1), (0, 1), and (1, 0).

D

On a coordinate plane, 2 quadrilaterals are shown. The larger quadrilateral has points (negative 5, 3), (1, 3), (4, 0), (negative 2, 0). The smaller quadrilateral has points (negative 0.5, 0), (negative 1, 2), (1, 2), (1.5, 0).

20

Triangle STV was dilated with the origin as the center of dilation to form S'T'V'.

A

One-third

B

Two-thirds

C

Three-halves

D

Three

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