Apply Properties of Similar Triangles

Determine if the following triangles are similar: Triangle XYZ has side lengths of 4 cm, 6 cm, and 8 cm, and Triangle UVW has side lengths of 6 cm, 9 cm, and 12 cm. Are the triangles similar?

• Not sure

• Maybe

• Yes

• No

Are Triangle PQR with side lengths 3 cm, 4 cm, and 5 cm, and Triangle STU with side lengths 6 cm, 8 cm, and 10 cm similar triangles?

• Maybe

• No

• Yes

• Not sure

Which statement about the triangles at the right is true?

• ΔABC is not similar to ΔADF

• ΔABC is similar to ΔADF

• ∠BAC is not congruent to ∠DAF

• ΔABC is congruent to ΔADF

Which of the following are properties of similar figures (or dilated figures)? Select all that apply.

• Corresponding angles are enlarged or reduced

• Corresponding side lengths are proportional

• Figures are the same size, but can different shapes

• Corresponding side lengths are equal

• Corresponding angles are equal (or congruent)

The two figures are similar. What is the scale factor going from the smaller figure to the larger figure?

• 2

• 3

• 1/2

• 1/3

Which point on the graph is the center of dilation?

• A

• B

• C

• R

• B'

Even though the lengths of images can change in a dilation, the ratios of their lengths have to be...

• congruent

• proportional/equivalent

• less than 1

• greater than 1

A SCALE FACTOR is...

• a number that when added, determines how much larger or smaller an image gets

• a number that when subtracted, determines how much larger or smaller an image gets

• a number that when multiplied, determines how much larger or smaller an image gets

• a number that when divided, determines how much larger or smaller an image gets

The images show a dilation of a cartoon image. What scale factor was used to create the dilation?

• 6

• 4

• 2

Two triangles are shown (blue and yellow). The ratio of vertical length to horizontal length in the largest triangle is \(\frac{6}{8}\). Which one of the following statements is true?

• The two triangles are NOT SIMILAR because they are not the same size.

• The two triangles are SIMILAR because when comparing the ratio of vertical length to horizontal length, they bot have equivalent ratios. (both equal to \(\frac{3}{4}\))

• The two triangles are CONGRUENT.

• It is impossible to determine if two images are similar or congruent from a grid.