Question

question 6 of 10
kira drew \\( \triangle p q r \\) and \\( \triangle s t u \\) so that \\( \angle p \cong \angle s, \angle q \cong \angle t, p r=12 \\), and \\( s u=3 \\).
are \\( \triangle p q r \\) and \\( \triangle s t u \\) similar? if so, identify the similarity postulate or
theorem that applies.
a. similar - aa
b. cannot be determined
c. similar - sas
d. similar - sss

Explanation:

The AA (Angle - Angle) similarity postulate states that if two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. In \(\triangle PQR\) and \(\triangle STU\), we are given that \(\angle P\cong\angle S\) and \(\angle Q\cong\angle T\). The lengths of \(PR = 12\) and \(SU=3\) are just additional information. Since we have two pairs of congruent angles, the AA similarity postulate applies.

Answer:

A. Similar - AA