Question

"Which theorem or postulate proves the two triangles are similar?

A) AA Postulate
B) AS Postulate
C) SAS Theorem
D) SSS Theorem"

Answer 1

A. AA Postulate

You can see that the bottom lines of the two of the overlapping triangles are parallel. That the bottom left angles of both triangles are congruent (because they are corresponding angles in parallel lines). In addition, they share the top angle, therefore it's proven by the AA Postulate

Answer 2

(A) AA Postulate

Explanation:

From the given figure, it can be seen that PQ is parallel to BC, therefore

∠APQ=∠ABC (If two lines are parallel, then the corresponding angles are equal)

Thus, from ΔAPQ and ΔABC, we have

∠APQ=∠ABC (If two lines are parallel, then the corresponding angles are equal)

∠PAQ=∠BAC (Common)

therefore, by AA postulate

ΔAPQ is similar to ΔABC.

Hence, option A is correct.