## About Isosceles Triangle

Triangle in which two sides are equal is called Isosceles triangle.

Out of three sides in Isosceles triangle, two sides are equal in length. Because of this two angels will be equal in isosceles triangle.

Following is a diagram of isosceles triangle.

### Terminology

- Leg – Equal sides are called legs. (In the above figure, AC and BC are legs)
- Base – Unequal side is called base. (In the above figure, AB is base)

## Properties of Isosceles Triangle

### Property 1

In Isosceles triangle, two sides are equal in length.

### Property 2

In Isosceles triangle, two angles opposite to the two equal sides are equal.

### Property 3

In Isosceles triangle, altitude to the base is always perpendicular to the base.

### Property 4

In Isosceles triangle, altitude to the base bisects the base. Meaning, altitude cuts the base into two equal halves.

### Property 5

In Isosceles triangle, circumcenter lies on the altitude to the base.

Circumcircle is the circle that touches all the three vertices of a triangle. Circumcenter is the center of circumcircle.

### Property 6

In Isosceles triangle, incenter lies on the altitude to the base.

Incircle is a circle which touches all the sides of the triangle. Incenter is the center of incircle.

### Property 7

In Isosceles triangle, centroid lies on the altitude to the base.

### Property 8

In Isosceles triangle, orthocenter lies on the altitude to the base.