Question

Prove that in a triangle, if square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.

Answer 1

Given: A triangle ABC in which AC2 = AB2 + BC2.
To Prove: ∠B = 90°.
Construction: We construct a ΔPQR right-angled at Q such that
PQ = AB and QR = BC
Proof: Now, from ΔPQR, we have,

Now, in ΔABC and ΔPQR,