An **Isosceles triangle** is one that has at least two sides of equal size. The figure below shows two examples.

## Parts of an Isosceles Triangle

The congruent edges of an isosceles triangle that has only two sides are called legs. The base is the third side. The vertex angle is the angle that lies opposite the base, while the angles that lie opposite the legs are the base angles.

## The length of an **Isosceles triangle**

An isosceles triangle’s height is determined by the perpendicular line segment that runs from the base to the opposing vertex.

We can use the Pythagorean Theory to find the following relationships between the base, legs and height of an Isosceles Triangle:

## Base angles for an isosceles triangle

An isosceles triangle’s base angles are equal in measurement. See triangle ABC below.

ABC ABC, which is the height of triangle ABC, is AB AC. ABC can be divided by drawing line segment AD. This is the height of triangle ABC.

is calculated using the Pythagorean Theory, where l represents the length of each leg. This is the ADBADC formula for congruent triangles based on the Side-Side-Side theory. Since congruent parts of congruent triangulars also have congruent parts, BC.

## Symmetry in an Isosceles triangle

An line illustrating symmetry also describes the altitude of an Isosceles Triangle.

Leg AB reflects from leg AC to leg AD at different altitudes. Similar to leg AB, leg AC also reflects back at leg AB. Base BC mirrors onto itself when it is reflecting across the altitude.

## 45-45-90 Triangles

The base angles of an **Isosceles triangle** are 45deg. This makes it a special triangle, called a 45deg 45deg-90deg triangle. The hypotenuse is the length of the base. It’s longer than its leg.

## Apothem for a regular polygon

As shown in the figure below, the height of a regular polygon can also be used to indicate the height of an **Isosceles triangle** formed by the center of the polygon and one side.

The height of the isosceles triangle BCG in the regular pentagon ABSDE is an indication of the polygon