Question

question 9 of 10
is △pqr ≅ △stu? if so, name the congruence postulate that
applies.

given:
∠p ≅ ∠s
∠q ≅ ∠t
pq ≅ st

a. congruent - asa
b. might not be congruent
c. congruent - sss
d. congruent - sas

Explanation:

Step1: Recall ASA Postulate

ASA (Angle - Side - Angle) postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Step2: Analyze Given Information

We are given that $\angle P\cong\angle S$, $\angle Q\cong\angle T$ and $PQ\cong ST$. In $\triangle PQR$ and $\triangle STU$, the side $PQ$ is between $\angle P$ and $\angle Q$, and the side $ST$ is between $\angle S$ and $\angle T$. So, two angles and the included side of $\triangle PQR$ are congruent to two angles and the included side of $\triangle STU$. By ASA postulate, $\triangle PQR\cong\triangle STU$.

Answer:

A. Congruent - ASA