# 8.10.2. Converse of Pythagoras Theorem

Given that

- Ayes
- Bno

### Example

Given that

### Solution

Step 1: Find the length of

Use Pythagoras' theorem, which states that the square of the length of a right-angled triangle's hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Substitute the known lengths in

Step 2: Find the length of

Use Pythagoras' theorem. Substitute the known lengths in

Step 3: Determine if

The converse of Pythagoras' theorem states that if the square of the length of a side is equal to the sum of the squares of the other two sides, then the angle opposite to this side is a right angle.

Since