Dilations, Congruency and Similarity

Let triangle XYZ be the dilated image of triangle ABC with a scale factor of k = 3. Which of the following is the correct center of dilation?

• (0, 0)

• (4, 1)

• (-5, 5)

• (1, 4)

The triangles are similar, solve for the question mark.

• 8

• 12.5

• 18

• 24

A scale factor of less than one means

• that the image will be larger than the pre-image.

• That the image will be the same as the pre-image.

• That you need to subtract that amount off  of each side.

• That the image will be a reduction of the pre-image.

What is the value of X?

• X=4

• X=6

• X=3

• X=2

A dilation of a figure is ___________.

• Congruent

• Similar

• Neither congruent nor similar

• Not proportional

Which of the following do not preserve congruence?

• reflections

• translations

• rotations

• dilations

Answer explanation

Dilations change size so they do not stay the same size...aka they do not preserve their size or congruence.

What is the rule for the dilation pictured below?

• (x, y) → (½x, ½y)

• (x, y) → (x + 2, y + 2)

• (x, y) → (2x, 2y)

• (x, y) → (2x, 3y)

Which is a true statement?

• Figure 1 is similar to Figure 2.

• Figure 1 is congruent to Figure 2.

• Figure 1 is both similar and congruent to Figure 2.

• Figure 1 is neither similar nor congruent to Figure 2.

Tell whether the two figures are congruent or similar.

• Congruent, because their sides are the same.

• Congruent, because their sides are proportional.

• Similar, because their sides are the same.

• Similar, because their sides are proportional.

• They are neither congruent or similar.

Tell whether the two figures are congruent or similar.

• Congruent, because their sides are the same.

• Congruent, because their sides are proportional.

• Similar, because their sides are the same.

• Similar, because their sides are proportional.

• They are not congruent or similar.