## Definition of an isosceles triangle

Isosceles triangles have at least two sides that are exactly the same length. This forces two of their angles to also be acute angles of exactly the same size.

### What is a triangle?

More geometry

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In this blue triangle, the two longer sides are the same length, which forces the two bottom angles to be the same size.

## Equilateral triangles

If the third side is also the same length as the first two sides, then the triangle is an equilateral triangle. All equilateral triangles have to be isosceles (eye-SAH-suh-leez) triangles, but not all isosceles triangles are equilateral.

### More about equilateral triangles

## Perimeter of isosceles triangles

Isosceles triangles, like other triangles, have a perimeter and an area. You can find out the perimeter of an isosceles triangle by adding together the length of all three sides. It’s harder to find out the area.

### What is perimeter?

What is area?

## How to find the area

To find the area of an isosceles triangle, start by drawing a line down the middle, from the top point to the middle of the bottom side. You’ll notice that an isosceles triangle has bilateral symmetry – that will be useful. Now you have two smaller triangles, but they’re exactly the same size, each half the area of the original triangle.

### What is bilateral symmetry?

When are things perpendicular?

What is a right triangle?

The line you drew down the middle is perpendicular to the bottom side of the triangle, so those two lines meet at right angles, forming two right triangles that are the same size. Because each of these right triangles makes half of a rectangle, you can imagine moving one of them, turning it upside down, and putting it against the other one to make a rectangle. Now it is easy to find the area of that rectangle if you know the height of the isosceles triangle and how wide the bottom is.

### What is the Pythagorean Theorem?

But suppose you only know the lengths of the three sides, and not how long the center line is? No problem. You can calculate the height of the center line using the Pythagorean Theorem, because half of an isosceles triangle is a right triangle.

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