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

Answer:

To prove

∠ABC = ∠PQR

Using euclidean distance, Length of each side can be found as

$AB=\sqrt{65} ,BC=\sqrt{45} ,CA=\sqrt{50} \\PQ=\sqrt{65} ,QR=\sqrt{45} ,RP=\sqrt{50}$

As can be seen

AB ≅ PQ

BC ≅ QR

CA ≅ RP

As all the sides of ΔABC are equal and congruent to ΔPQR, this Proves that measure of all angles inside both triangles must be equal.