Converse of Pythagoras Theorem class 10th
Theorem 6.9 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. Proof:- Given : - In a △ABC in which AC 2 =AB 2 +B C 2 Prove That : -∠B=90° Construction :- A △PQR right triangle at Q such that PQ=AB and QR=BC (In figure) Now, from △PQR , we have: PR 2 =PQ 2 +QR 2 (Pythagoras Theorem as ∠Q=90°) PR 2 =AB 2 +B C 2 (By construction)...(1) But AC 2 =AB 2 +B C 2 (Given) ...(2) so, AC=PR [from(1) and (2)]...(3) Now, in △ABC and △PQR, AB=PQ (by construction) BC=QR (by construction) ...