# Congruence

Rules for congruence in triangles for GCSE maths

HideShow resource information

## Congruence

Two shapes are congruent if they are identical in shape and size

There are four rules that are used to prove that a pair of triangles are congruent:

1 of 5

## All three pairs of sides are equal (SSS)

When all three pairs of sides are equal, the triangles are congruent as both triangles have all sides of the same length.

This rule is written as 'SSS' for 'side side side'

2 of 5

## Right angle, Hypotenuse and Side are equal

When both triangles are right angled and the lengths of the hypotenuse and the other side are equal to each other, the triangles are congruent.

e.g. when h1=h2 and s1=s2 and both are right angled triangles

This rule is written as 'RHS' for 'right angle hypotenuse side'

3 of 5

## Two Sides are equal and the corresponding Angles a

When  two pairs of corresponding sides are equal and the angles between the pairs of sides are also equal, then the triangles are congruent

This rule is written as 'SAS' for 'side angle side'

4 of 5

## Two pairs of Angles and a pair of Sides are equal

When two pairs of angles and a pair of corresponding sides are equal, the triangles are congruent.

This rule is written as 'AAS' for 'angle angle side'

5 of 5