# What is an Isosceles Triangle

By the end of this lesson, you will be able to

- define isosceles triangle.
- calculate the perimeter and area of an isosceles triangle.
- demonstrate examples of isosceles triangle.
- relate isosceles triangle to scalene triangle.

## Isosceles Triangle

The triangle having two sides of equal length is called isosceles triangle. Another way ..., the triangle that has two equal length of sides is called isosceles triangle.

An isosceles triangle

Thus, there are two equal sides of an isosceles triangle. Equivalently, the two angles opposite its two equal sides are always equal measuring.

The two equal sides are known as legs while the third side called the base. This is a special type of triangle in terms of side.

## Vertex Angle

The angle included by the two equal legs or sides of an isosceles triangle is an vertex angle.

The vertex for the vertex angle opposite the base is sometimes called the appex.

An isosceles triangle showing its base and equal sides.

## Base Angles

In an isosceles triangle, the angles included by one of the legs (or equal sides) and the base are base angles.

One can determine all angles depending upon a given angle for an isosceles triangle.

Although there is a seperate formula to finding out the area of an isosceles triangle, but one can also evaluate the area applying the formula used for scalene triangle.

### Isosceles Triangle Example

## Perimeter of Isosceles Triangle

The sum of base and twice the equal side of an isosceles triangle is called the perimeter.

Let BC = b, AC = a and AB = a in an isosceles △ABC.

Then the perimeter,

P = (a + a + b) unit

∴ P = (2a+b) unit

## Area of Isosceles Triangle

Suppose, base BC = b, AC = a and AB = a in an isosceles △ABC.

Draw AD⊥BC.

The perpendicular drawn from the vertex to base divides the base into two equal parts.

∴ BD = 12 BC

∴ BD = b2

From the right △ABD, it can be written as

AD^{2} = AB^{2} - BD^{2}

or, AD^{2} = a^{2} - b^{2}4

or, AD^{2} = 4a^{2} - b^{2}4

or, AD = √4a^{2} - b^{2}√4

or, AD = √4a^{2} - b^{2}2

∴ △ABC = 12 BC.AD

or, △ABC = 12 b. √4a^{2} - b^{2}2

∴ △ABC = b4 √4a^{2} - b^{2}

If the length of the base is b, equal side is a and the area is A,

A = b4 √4a^{2} - b^{2} square unit.