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 Congruence Postulates

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 triangles are congruent. SSS (Side - Side - Side) postulate states that if three sides of one triangle are congruent to three sides of another triangle, the triangles are congruent. SAS (Side - Angle - Side) postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the 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 $\triangle STU$, $\angle P$ and $\angle Q$ are two angles with included side $PQ$. In $\triangle STU$, $\angle S$ and $\angle T$ are two angles with included side $ST$. So, two angles and the included side of $\triangle PQR$ are congruent to two angles and the included side of $\triangle STU$. This matches the ASA congruence postulate.

Answer:

A. Congruent - ASA