Question

is $\triangle pqr \cong \triangle stu$? if so, name the congruence postulate that applies.

given:
$\angle p \cong \angle s$
$\angle q \cong \angle t$
$\overline{pq} \cong \overline{st}$

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

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.

Step2: Analyze Given Information

We are given that $\angle P\cong\angle S$, $\angle Q\cong\angle T$ and $\overline{PQ}\cong\overline{ST}$. In $\triangle PQR$ and $\triangle STU$, the side $\overline{PQ}$ is between $\angle P$ and $\angle Q$, and the side $\overline{ST}$ is between $\angle S$ and $\angle T$. So we have two angles and the included side of $\triangle PQR$ congruent to two angles and the included side of $\triangle STU$. This matches the ASA congruence postulate.

Answer:

D. Congruent - ASA