1. What is the measure of angle A'B'C?

a. 20°
b. 40°
C. 60°
d. 80°

B

Step-by-step explanation:

Compare triangle ABC with triangle A'B'C. Let's try to prove that they're similar.

BC = 6 + 3 = 9 units

B'C = 6 units

BC/B'C' = 9/6 = 3/2 = 1.5

AC = 2 + 4 = 6 units

A'C = 4 units

AC/A'C = 6/4 = 3/2 = 1.5

These two pairs of corresponding sides have the same ratio, so that's promising.

Also notice that angle BCA = angle B'CA'. So, by SAS Similarity Theorem, we know that triangles ABC and A'B'C are similar.

By definition, similar triangles have the same corresponding angles.

Angle ABC corresponds to angle A'B'C, so they're equal. Since angle ABC = 40 degrees, then angle A'B'C = 40 degrees, as well.

Hope this helps!

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