Question

question 7 of 10
is \\( \triangle p q r \cong \triangle s t u \\) ? if so, name the congruence postulate that applies.
given:
\\( \angle p \cong \angle s \\)
\\( \angle q \cong \angle t \\)
\\( \overline{p q} \cong \overline{s t} \\)
a. congruent - sas
b. might not be congruent
c. congruent - sss
d. congruent - asa

Explanation:

The ASA (Angle - Side - Angle) congruence 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. In \(\triangle PQR\) and \(\triangle STU\), \(\angle P\cong\angle S\), \(\overline{PQ}\cong\overline{ST}\), and \(\angle Q\cong\angle T\). Here, \(\overline{PQ}\) is the included side between \(\angle P\) and \(\angle Q\) in \(\triangle PQR\), and \(\overline{ST}\) is the included side between \(\angle S\) and \(\angle T\) in \(\triangle STU\).

Answer:

D. Congruent - ASA