Question

in the figure below, the measure of ∠m is 33° and the measure of ∠p is 147°. determine how the triangles can be shown to be similar.
a. the triangles are not similar to each other.
b. the triangles are similar by sss.
c. the triangles are similar by sas.
d. the triangles are similar by aa.

Explanation:

Step1: Find the measure of ∠s

Since ∠p + ∠s = 180° (linear - pair of angles), and ∠p = 147°, then ∠s=180° - 147° = 33°.

Step2: Analyze angle - angle similarity

We know that ∠m = 33°, so ∠m = ∠s. Also, the two triangles have a common angle.
By the AA (Angle - Angle) similarity criterion, if two angles of one triangle are equal to two angles of another triangle, then the two triangles are similar.

Answer:

D. The triangles are similar by AA.