In the isosceles triangle below, cm, cm, and cm. Is a right-angled triangle?
Step 1: Find the length of .
First, find the length of . Since is isosceles and , then bisects . Therefore,
Then use Pythagoras's theorem. Substitute the known lengths in , and solve for the length of .
Step 2: Find the length of .
Then use Pythagoras's theorem to find the length of .
Substitute the known lengths in , and solve for the length of .
Approximate to the nearest hundredth.
Then add to find the length of .
Step 3: Determine if is a right-angled triangle.
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. For ,
Since , then and is not a right-angled triangle.