Question

question 3 of 10
is △abc ~ △def? if so, identify the similarity postulate or
theorem that applies.

a. similar - aa
b. similar - sss
c. similar - sas
d. cannot be determined

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). For \(\triangle ABC\), we know \(\angle B = 30^\circ\) and \(\angle A = 88^\circ\). So \(\angle C=180^\circ - 30^\circ - 88^\circ = 62^\circ\). For \(\triangle DEF\), \(\angle E = 30^\circ\) and \(\angle D = 88^\circ\), so \(\angle F = 180^\circ - 30^\circ - 88^\circ = 62^\circ\).

Step2: Apply AA similarity

We see that \(\angle A=\angle D = 88^\circ\) and \(\angle B=\angle E = 30^\circ\). By the AA (Angle - Angle) similarity postulate, if two angles of one triangle are congruent to two angles of another triangle, the triangles are similar.

Answer:

A. Similar - AA