## The Lesson

An isosceles triangle is a triangle with two equal sides and two equal angles across from them.**Note:**The lines through the two sides of the triangle in the image above indicate they are of equal length. The two arcs indicate the two angles are equal.

## Dictionary Definition

The Merriam-Webster dictionary defines an isosceles triangle as "a triangle in which two sides have the same length."## Real Examples of Isosceles Triangles

Below are real examples of isosceles triangles.In each case

- 2 sides are the same length.
- 2 angles are the same.

## The Parts of an Isosceles Triangle

An isosceles triangle has 2 equal sides. These sides are called**legs**.

The third side is called the

**base**.

An isosceles triangle has 2 equal angles. These are the angles between each leg and the base. They are called

**base angles**.

The angle between the legs is called the

**vertex angle**.

## Properties of Isosceles Triangles

## The Symmetry of Isosceles Triangles

An isosceles triangle has 1 line of symmetry. It is the line that goes through the vertex angle and the midpoint of the base.## What's in a Name?

'Isosceles' comes from the Greek words 'isos', meaning 'equal', and 'skelos', meaning 'leg'. 'Isosceles' means 'equal legs', as the two equal sides are known as legs.## Interior Angles of an Isosceles Triangle

Two of the interior angles of an isosceles triangle are equal. There are two different angles in an isosceles triangle: the base angle and the vertex angle.We also know that the interior angles of any triangle always add up to 180°.

Knowing either the base angle or the vertex angle allows the other to be found.

In words,

**Vertex angle = 180° − (2 × Base angle)**

**Base angle = (180° − Vertex angle) ÷ 2**

## Interactive Game on the Types of Triangle

**the types of triangle**.