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Isosceles Triangles (Mathematics Glossary)

What Is an Isosceles Triangle?

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."

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.

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.

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
Curriculum
Geometry Lessons
Interactive Test
  show
 


Here's a second test on isosceles triangles.
Here's a third test on isosceles triangles.
Note

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

Other Types of Triangle

Isosceles triangles are one type of triangle.

There are also: