# Are all isosceles triangles equilateral?

##### 1 Answer

Jan 19, 2016

No.

*Isosceles* triangles are those that have two sides to be of equal length, while equilateral triangles are those that have all three sides of equal length.

#### Explanation:

*Theorem*

There exist *isosceles* triangles that are **not** *equilateral*.

*Proof*

A triangle with a base of 10 cm and two other sides each of 20 cm is *isosceles*, but not *equilateral*.

This counter example proves that not all *isosceles* triangles are *equilateral*.