# What is an Isosceles Triangle? - Definition, Properties & Theorem

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• 0:05 What is an Isosceles Triangle?
• 0:34 Properties of…
• 2:27 Isosceles Triangle Theorem
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Lesson Transcript
Instructor: Joseph Vigil
In this lesson, you'll learn how an isosceles triangle's sides and angles make it unique. You'll also learn the theorem of isosceles triangles. Then, you can test your knowledge with a brief quiz.

## What is an Isosceles Triangle?

An isosceles triangle is a triangle with two congruent sides and congruent base angles. Congruent means equal. For example, this is an isosceles triangle:

And although this triangle points a different way, it's also an isosceles triangle:

No matter which direction the triangle's apex, or peak, points, it's an isosceles triangle if two of its sides are congruent.

Note the hash marks that indicate congruency. Any sides or angles with the same number of hashes through them are congruent.

## Properties of Isosceles Triangles

Of course, the main property of isosceles triangles is their two congruent sides. In addition, all isosceles triangles also have congruent base angles.

This property holds true for all isosceles triangles, no matter which direction their apexes point.

If we know the measure of either of the base angles, then we can determine the measure of the third (apex) angle. Since the angles of a triangle add up to 180 degrees, the third angle is 180 minus two times a base angle, making the formula for the measure of an isosceles triangle's apex angle:

A = 180 - 2b

Where A is the apex measure and b is the measure of one base angle.

So if a base angle in an isosceles triangle measured 58 degrees, we could plug that into our formula to determine the measure of the apex angle:

A = 180 - (2 * 58)

A = 180 - 116

A = 64

The measure of the triangle's apex angle is 64 degrees.

Likewise, if we know the measure of the apex angle, we can find the measures of both base angles based on this same understanding. Singe the angles add up to 180 degrees, 180 minus the apex angle will result in the sum of both base angles. Then we simply divide this by two to find the measure of each base angle.

2b = (180 - A)

If an apex angle in an isosceles triangle measures 72 degrees, we could use that in our formula to determine the measure of both base angles.

2b = (180 - 72)

2b = 108

b = 108/2

b = 54

The measure of each base angle in the triangle is 54 degrees.

## Isosceles Triangle Theorem

The theorem of an isosceles triangle involves three statements:

Statement 1: An isosceles triangle's altitude, or line segment that extends from the triangle's apex to its base's midpoint, is perpendicular to its base.

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