Q28 of 40 Page 1

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

Consider ΔABC such that AC2 =AB2 +BC2

To prove : ∠B = 90°


Construction : We construct another ΔPQR right angled at Q such that PQ = AB and QR = BC


In ΔPQR , by Pythagoras theorem, we have




In Δ ABC & ΔPQR


AB = PQ [by construction]


BC = QR [by construction]


AC = PR [Proved above]



∠B = ∠Q = 90° [by CPCT]


Hence proved


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