Pythagoras Theorem

When a triangle has a right angle (90°) and squares are made on each of the 3 sides, then the biggest square has the exact same area as the other 2 squares put together!

Pythagoras Theorem can be written in one short equation:

a2 + b2 = c2

Where:

  • c is the longest side of the triangle
  • a and b are the other 2 sides
Pythagoras Theorem Triangle

Definition

The longest side of the triangle is called the “hypotenuse”, so the formal definition is:

Pythagoras Theorem Triangle 2

In a right angled triangle:

The square of the hypotenuse is equal to the sum of the squares of the other 2 sides.

Is This Useful?

If we know the lengths of 2 sides of a right angled triangle, we can find the length of the third side.

It only works on right angled triangles!

How Do I Use it?

Write it down as an equation

Example

Find b!

Pythagoras Theorem Triangle Example

a2 + b2 = c2

b2 = c2 a2

b2 = 132 52

b2 = 169 – 25

b2 = 144

b = 12

Learn More

Solving SSS Triangles

Solving SSA Triangles

Solving SAS Triangles

How To Find if Triangles are Congruent

Algebra Index

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