1. Pythagoras’ Theorem – Outcomes
Solve problems using Pythagoras’ theorem.

2. Solve Problems
Pythagoras’ theorem states that the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides.
How can you tell which side is the hypotenuse?
Pythagoras’ theorem:
𝑐 2 = 𝑎 2 + 𝑏 2

3. Solve Problems
Pythagoras’ theorem only works for right-angled triangles.
We can test it on a triangle to determine whether or not it is right-angled.
Which of the following triangles are right-angled? a) c) b)
b and c

4. Solve Problems Pythagoras’ theorem is used when:
you know two side lengths of a right-angled triangle,
you need to find the length of the remaining side.
e.g. what is the length of the hypotenuse?

5. Solve Problems
Find the length of the hypotenuse in each of the following triangles to one decimal place: a) b)
7.6
10.4
6.7
7.0 d) c)

6. Solve Problems
Sometimes we know the hypotenuse, but not one of the other sides.
What is the missing side length in each of the following triangles? a) b) a) b) c)
d) 5.9 c) d)