Question

is △abc ~ △xyz? if so, identify the similarity postulate or theorem that applies.
a. similar - sss
b. similar - aa
c. similar - sas
d. cannot be determined

Explanation:

Step1: Analyze triangle angles

In $\triangle ABC$, $\angle B = 30^\circ$, $\angle C = 85^\circ$. So $\angle A = 180^\circ - 30^\circ - 85^\circ = 65^\circ$.
In $\triangle XYZ$, $\angle Y = 30^\circ$, $\angle Z = 85^\circ$. So $\angle X = 180^\circ - 30^\circ - 85^\circ = 65^\circ$.

Step2: Identify similarity criterion

Two angles of $\triangle ABC$ match two angles of $\triangle XYZ$ ( $\angle B = \angle Y = 30^\circ$, $\angle C = \angle Z = 85^\circ$ ). By AA (Angle - Angle) similarity postulate, if two angles of one triangle are equal to two angles of another triangle, the triangles are similar.

Answer:

B. Similar - AA