# How To Find if Triangles are Congruent

Two triangles are congruent if they have: - exactly the same three sides and
- exactly the same three angles.
But we don't have to know all three sides and all three angles ...usually |

There are five ways to find if two triangles are congruent: **SSS**, **SAS**, **ASA**, **AAS** and **HL**.

## 1. SSS *(side, side, side)*

**SSS** stands for "side, side, side" and means that we have two triangles with all three sides equal.

For example:

is congruent to: |

*(See Solving SSS Triangles to find out more) *

If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.

## 2. SAS *(side, angle, side)*

**SAS** stands for "side, angle, side" and means that we have two triangles where we know two sides and the included angle are equal.

For example:

is congruent to: |

*(See Solving SAS Triangles to find out more) *

If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.

## 3. ASA *(angle, side, angle)*

**ASA** stands for "angle, side, angle" and means that we have two triangles where we know two angles and the included side are equal.

For example:

is congruent to: |

*(See Solving ASA Triangles to find out more)*

If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

## 4. AAS *(angle, angle, side)*

**AAS** stands for "angle, angle, side" and means that we have two triangles where we know two angles and the non-included side are equal.

For example:

is congruent to: |

*(See Solving AAS Triangles to find out more)*

If two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

## 5. HL *(hypotenuse, leg)*

This one applies only to right angled-triangles!

or |

**HL** stands for "**H**ypotenuse, **L**eg" (the longest side of a right-angled triangle is called the "hypotenuse", the other two sides are called "legs")

It means we have two right-angled triangles with

- the
**same length of hypotenuse**and - the
**same length for one of the other two legs**.

It doesn't matter which leg since the triangles could be rotated.

For example:

is congruent to: |

*(See Pythagoras' Theorem to find out more)*

If the hypotenuse and one leg of one right-angled triangle are equal to the corresponding hypotenuse and leg of another right-angled triangle, the two triangles are congruent.

## Caution ! Don't Use "AAA" !

**AAA** means we are given all three angles of a triangle, but no sides.

**This is not enough information to decide if two triangles are congruent!**

Because the triangles can have the same angles but be **different sizes**:

is not congruent to: |

Without knowing at least one side, we can't be sure if two triangles are congruent.