I have a question about a triangle proof question from Philips Exeter Academy

Question

. Let A = (0, 0), B = (8, 1), C = (5, −5), P = (0, 3), Q = (7, 7), and R = (1, 10). Prove that angles ABC and P QR have the same size.

Answer 1

Hi Walter,

Use the distance formula

d = √((x₂ -x₁)² +(y₂-y₁)² ) to find the lengths of each side of triangle ABC, then do the same for the lengths of triangle PQR.

Then, show that the corresponding sides of triangles ABC and PQR are congruent.

AB ≅ PQ, BC ≅ QR, AC ≅ PR because they have the same lengths.

By SSS, triangle ABC ≅ triangle PQR. Since the triangles are congruent, corresponding angles are congruent.