^{PYTHAGORAS' THEOREM}

In any right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Thus in the above right-angled triangle, a^{2} + b^{2} = c^{2}

^{CONVERSE}

^{If a triangle of sides a, b and c is such that }

a^{2} + b^{2} = c^{2}

^{... then the triangle is right-angled.}

**Example 1**

A triangle has sides of length 6 cm, 8 cm and 9 cm.

Is it right-angled?

**Answer**

First pick the two shorter sides, square them and add

6^{2} + 8^{2} = 36 + 64 = 100

Then square the longest side

9^{2} = 81

So 6^{2} + 8^{2} ≠ 9^{2} and the triangle is therefore **not right-angled.**

**Example 2**

A triangle has sides of length 5 cm, 13 cm and 12 cm.

Is it right-angled?

**Answer**

First pick the two shorter sides, square them and add

5^{2} + 12^{2} = 25 + 144 = 169

Then square the longest side

13^{2} = 169

So 5^{2} + 12^{2} = 13^{2} and the triangle is therefore **right-angled.**