Quiz about Properties of Similarity Transformations

Question 1

Which statement is true of rectangles Y and Z?

Accepted Answer

They are not similar because their corresponding side lengths are not proportional.

Answer

They are congruent because their corresponding angles are congruent.

Answer

They are similar because their corresponding angles are congruent.

Answer

They are similar because their corresponding side lengths are proportional.

Question 2

Which statement is true of triangles P and Q?

Accepted Answer

They are similar because their corresponding angles are congruent and their corresponding side lengths are proportional.

Answer

They are similar because their corresponding angles have proportional measures and their corresponding sides are congruent.

Answer

They are not similar because their corresponding angles are congruent.

Answer

They are not similar because their corresponding side lengths are not proportional.

Question 3

Which statement describes the relationship, if any, that exists between triangle KLM and triangle NPQ?

Accepted Answer

They are similar because their corresponding angles are congruent and their corresponding side lengths are in the ratio 2/1 from Triangle KLM to NPQ .

Answer

They are similar because their corresponding angles are congruent and their corresponding side lengths are in the ratio 3/2 from Triangle KLM to NPQ .

Answer

They are not similar because their corresponding angles are not congruent.

Answer

They are not similar because their corresponding side lengths are not proportional.

Question 4

Which figure is similar to the parallelogram? (Figures may not be drawn to scale.)

Accepted Answer

Option D is correct

Answer

A.

Answer

B.

Answer

C.

Question 5

Which statement is true of triangles QRS and MNP?

Accepted Answer

They are similar because their corresponding angles are congruent and their corresponding side lengths are proportional.

Answer

They are congruent because their corresponding angles are congruent and their corresponding side lengths are congruent.

Answer

They are not similar because their corresponding angles are not congruent.

Answer

They are not similar because their corresponding side lengths are not proportional.

Question 6

Rectangle R was dilated to form rectangle R' .

Which is the scale factor of the dilation?

Accepted Answer

$$\frac{5}{2}$$

Answer

$$\frac{5}{4}$$

Answer

$$\frac{2}{1}$$

Answer

$$\frac{5}{1}$$

Question 7

Triangle T was dilated to form triangle T' .

Which ratio is the correct scale factor? (Figures not drawn to scale.)

Accepted Answer

$$\frac{5}{9}$$

Answer

$$\frac{5}{18}$$

Answer

$$\frac{1}{2}$$

Answer

$$\frac{9}{10}$$

Question 8

The smaller triangle was dilated to form the larger triangle. What is the value of x?

Accepted Answer

7.5

Answer

6.9

Answer

10

Answer

11

Question 9

The smaller triangle was dilated to form the larger triangle. What is the value of x?

Accepted Answer

14

Answer

10

Answer

11

Answer

15

Question 10

The unshaded trapezoid is the image of the shaded trapezoid after a series of transformations.

What is the value of x?

Accepted Answer

12

Answer

3

Answer

9

Answer

18

Question 11

Triangle ABC has been dilated about point A by a scale factor of 1/3.

What are the lengths, in units, of the three sides of triangle A'B'C' ?

Accepted Answer

10, 16, 13

Answer

10, 12, 13

Answer

90, 124, 97

Answer

90, 144, 117

Question 12

The parallelogram on the left was dilated by a scale factor of 2 about point P. It was then transformed in another way to produce the parallelogram on the right.

Which identifies the transformation that occurred after the dilation?

Accepted Answer

a translation of 9 units to the right

Answer

a translation of 3 units down

Answer

a reflection across the x-axis

Answer

a reflection across the y-axis

Question 13

Quadrilateral H' is the image of quadrilateral H after a sequence of transformations. If quadrilateral H' is congruent to quadrilateral H, which transformations could have been used?

Accepted Answer

a translation of 6 units down, a rotation, and then a reflection

Answer

a dilation by a scale factor of 2 followed by a reflection

Answer

a rotation followed by a dilation by a scale factor of 1/2

Answer

a reflection, a translation of 1 unit left, and then a dilation by a scale factor of 3

Question 14

Triangle QNP was dilated by a scale factor of 1/3 about point P. It was then transformed in another way to produce triangle Q'N'P'

Which identifies the transformation that occurred after the dilation?

Accepted Answer

a 90 degrees clockwise rotation about the origin

Answer

a 180 degrees clockwise rotation about the origin

Answer

a reflection across the x-axis

Answer

a reflection across the y-axis

Question 15

Which describes how triangle FGH could be transformed to triangle F'G'H' in two steps?

Which identifies the transformation that occurred after the dilation?

Accepted Answer

a dilation by a scale factor of 4 and then a reflection across the x-axis

Answer

a dilation by a scale factor of 3 and then a reflection across the x-axis

Answer

a dilation by a scale factor of 3 and then a 180 degrees rotation about the origin

Answer

a dilation by a scale factor of 4 and then a 180 degrees rotation about the origin

Question 16

A triangle is dilated by a scale factor of 1/5 and then rotated 90 degrees clockwise about the origin. Why is the image similar to the pre-image? Check all that apply.

Accepted Answer

The corresponding angles of the triangles are congruent.

Accepted Answer

The image is a reduction of the pre-image.

Accepted Answer

Neither the dilation nor the rotation change the shape of the triangle.

Answer

The corresponding sides of the triangles are congruent.

Answer

The corresponding sides of the image are 5 times as long as those of the pre-image.

Properties of Similarity Transformations

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