Similarity and Proportional Reasoning

Tell whether the two figures are similar. Explain your reasoning.

• Yes, similar because they are the same shape and side lengths are proportional.

• No, not similar because they are the same shape, but side lengths are not proportional.

• Yes, same shape

• No, different sizes

Are the following similar? Why or why not?

• Yes. All pairs of corresponding angles are congruent and the sides are proportional.

• No, the corresponding angles are not equal.

• No, the ratios of the corresponding sides are not equal.

What is the scale factor from the triangle to the left to the triangle on the right?

• 2

• 3/2

• 2/3

• 1/2

What is the scale factor from ΔDEF to ΔABC?

• 1/2

• 7/3

• 2

• 10/3

∆ABF~∆ACE. What is the length of CB?

• 7.2 units

• 4.05 units

• 20 units

• There is not enough information to determine the length of CB.

Given ∆ABC ~ ∆LMN, what is the length of segment AC?

• 11

• 12

• 22

• 24

What is the scale factor from ABCD to MNOP?

• 2/3

• 3/2

• 2

• 3

Sides in similar figures must be proportional.  

• True

• False 

What is the similarity statement for the triangle pair?

• ΔXYZ~ΔNEW

• ΔXZY~ΔNWE

• ΔZYX~ΔENW

• ΔYZX~ΔNWE

Choose the similarity statement for the triangles.

• ΔMNL ∼ ΔOPQ

• ΔNOM ∼ ΔPQL

• ΔLMN ∼ ΔPQO

• ΔMLN ∼ ΔPQO