Question

1. determine whether or not the pairs of triangles are similar and explain why.

a.
b.
c.

Explanation:

Step1: Check part a (AA similarity)

Two pairs of corresponding angles are marked congruent. By AA (Angle-Angle) similarity criterion, triangles are similar.

Step2: Check part b (Side ratios)

Calculate ratios of corresponding sides:
$\frac{4}{12} = \frac{1}{3}$, $\frac{3}{9} = \frac{1}{3}$, $\frac{8}{22} = \frac{4}{11}$
Since $\frac{1}{3}
eq \frac{4}{11}$, sides are not proportional. Triangles are not similar.

Step3: Check part c (AA similarity)

Two pairs of corresponding angles are marked congruent. By AA (Angle-Angle) similarity criterion, triangles are similar.

Answer:

a. The triangles are similar. Two pairs of corresponding angles are congruent, satisfying the AA similarity criterion.
b. The triangles are not similar. The ratios of corresponding sides are not equal ($\frac{4}{12}=\frac{1}{3}$, $\frac{3}{9}=\frac{1}{3}$, $\frac{8}{22}=\frac{4}{11}$), so the SSS similarity criterion is not met.
c. The triangles are similar. Two pairs of corresponding angles are congruent, satisfying the AA similarity criterion.