Question

1. prove that △xyz ~ △pqr using aa similarity, where ∠x = ∠p and ∠z = ∠r. fill in the missing statement.

statement: ∠x = ∠p
reason: given
△xyz ~ △pqr
aa similarity criterion
given
options:
a. ∠y = ∠q
b. ∠z = ∠r
c. ∠r = ∠y
d. ∠z = ∠q

Explanation:

Step1: Recall AA similarity criterion

For two triangles $\triangle XYZ$ and $\triangle PQR$ to be similar by AA (angle - angle) similarity criterion, two pairs of corresponding angles must be equal. We are already given that $\angle X=\angle P$ and $\angle Z = \angle R$.

Step2: Identify the missing angle - pair equality

The third - pair of angles for the AA similarity to hold should be $\angle Y=\angle Q$.

Answer:

a. $\angle Y=\angle Q$