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

To prove

∠ABC = ∠PQR

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

`AB=√(65) ,BC=√(45) ,CA=√(50) \\PQ=√(65) ,QR=√(45) ,RP=√(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.