# Isosceles Triangle

How to solve an isosceles triangle by using its definition: definition, 3 examples, and their solutions.

## Definition

### Definition

An isosceles triangle is a triangle

that has two congruent sides (= legs).

The non-congruent side is the base.

The two angles

that are adjacent to the base

are congruent.

## Example 1

### Example

### Solution

The given triangle is an isosceles triangle.

So these two angles are congruent.

So [3x + 25] = [55].

Move +25 to the right side.

Then 3x = 30.

Divide both sides by 3.

Then x = 10.

So x = 10.

## Example 2

### Example

### Solution

The given triangle is an isosceles triangle.

Then the bottom two angles are congruent.

So the bottom right angle is [4x + 3]º.

These three angles

are the interior angles of the given triangle.

So 2[4x + 3] + [3x - 2] = 180.

2(4x + 3) = 8x + 6

8x + 3x = 11x

+6 - 2 = +4

Move +4 to the right side.

Then 11x = 176.

Divide both sides by 11.

Then x = 16.

So x = 16.

## Example 3

### Example

### Solution

See the left triangle.

This is an isosceles triangle.

So the upper angle

is congruent to the bottom angle:

xº.

So the upper angle is

xº.

Next, see the right triangle.

This is also an isosceles triangle.

So the bottom left angle

is congruent to the bottom right angle:

70º.

So the bottom left angle is

70º.

70º is the exterior angle.

And the two xº angles

are the non-adjacent interior angles.

So [x] + [x] = [70].

x + x = 2x

2x = 70

Divide both sides by 2.

Then x = 35.

So x = 35.