Question

Given: QR || PT and QPR = ZSTR

Prove: APQR ~ ATSR

a) ∠A = ∠A (corresponding angles are equal)
b) ∠P = ∠S (corresponding angles are equal)
c) ∠Q = ∠T (corresponding angles are equal)
d) ΔAPQ ~ ΔATS (by angle-angle similarity)

Answer 1

To prove that the triangles APQR and ATSR are similar, you need to show that corresponding angles are equal and that the triangles have two pairs of equal angles. d) ΔAPQ ~ ΔATS by angle-angle similarity.

Step-by-step explanation:

To prove that APQR ~ ATSR, we need to show that ∠A = ∠A, ∠P = ∠S, ∠Q = ∠T, and ΔAPQ ~ ΔATS.

Since QR || PT and QPR = ZSTR (corresponding angles are equal), we have ∠A = ∠A and ∠P = ∠S (corresponding angles are equal).

Also, since QR || PT, we have ∠Q = ∠T (corresponding angles are equal).

Finally, ΔAPQ ~ ΔATS by angle-angle similarity.