Question

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

Answer 1

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

Here, we are given a triangle ABC with. We need to prove that

.

Now, we construct a triangle PQR right angled at Q such that and .

We have the following diagram.

Now, in, we have

…… (1)

But, it is given that

…… (2)

From equations (1) and (2), we get

…… (3)

From the above analysis in and, we have

Since, therefore

Hence,