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# Congruence: conditions for congruent triangles 0%

Summary

# Congruence: conditions for congruent triangles

## ​​In a nutshell

Congruent shapes are shapes that are exactly the same apart from rotational/mirror differences. There are four main conditions for two triangles to be congruent.

### Congruency

Two shapes are congruent if they have the same side lengths and the same angles. It doesn't matter if the shapes are rotated slightly differently or if they're mirrored.

## Congruency conditions

There are four ways to prove that two triangles are congruent.

#### example

SSS

All three sides of the triangle are the same

SAS

Two sides and the angle between them are the same

AS

Two angles and a corresponding side are the same

RHS

Both triangles have a right-angle, the same hypotenuse and other common side

##### Example 1

Are the two triangles shown congruent to one another?

At first glance, the two triangles look to be congruent due to the ASA rule - both triangles have angles of $40^\circ$ and $80^\circ$ and they both have a side of $2.2cm$.

However, upon closer inspection, this is not a case of ASA. This is because the two sides aren't corresponding.

The triangle to the left has a side length of $2.2cm$ that is between the two angles of $40^\circ$ and $80^\circ$.

The triangle to the right has a side length of $2.2cm$ that is not between the two angles of $40^\circ$ and $80^\circ$, so it's not the corresponding sides that are equal.

The triangles are NOT congruent.

## Want to find out more? Check out these other lessons!

Congruent shapes

FAQs

• Question: What are the four ways to prove two triangles are congruent?

Answer: SSS, SAS, ASA and RHS are the four ways to prove two triangles are congruent.

• Question: What does it mean for two shapes to be congruent?

Answer: Two shapes are congruent if they are exactly the same shape, just rotated and/or mirrored.

Theory

Exercises