# Isosceles Trapezoid: Property

How to use the properties of an isosceles trapezoid to solve the related problems: definition, 2 properties (angles, diagonals), 2 examples, and their solutions.

## Definition

### Definition

An isosceles trapezoid is a trapezoid

whose legs are congruent.

Just like an isosceles triangle,

its base angles are also congruent.

An isosceles trapezoid is also a trapezoid.

So an isosceles trapezoid

has all the properties of a trapezoid.

## Property: Angles

### Property

For an isosceles trapezoid,

two interior angles

that inscribe the same base

are congruent.

m∠1 = m∠1'

m∠2 = m∠2'

And two interior angles

that inscribe the same leg

are supplementary.

m∠1 + m∠2 = 180

m∠1' + m∠2' = 180

(This is also true for a trapezoid.)

## Example 1

### Example

### Solution

The given quadrilateral is an isosceles trapezoid.

∠A and ∠D are the interior angles

that inscribe the same left leg.

m∠D = 60

So m∠A + [60] = 180.

Move +60 to the right side.

Then m∠A = 120.

Write 120º on ∠A.

∠A and ∠B are the interior angles

that inscribe the same top base.

∠A is 120º.

So ∠B is 120º.

∠D and ∠C are the interior angles

that inscribe the same bottom base.

∠D is 60º.

So ∠C is 60º.

Write m∠A, m∠B, and m∠C.

So

m∠A = 120

m∠B = 120

m∠C = 60

is the answer.

## Property: Diagonals

### Property

For an isosceles trapezoid,

four segments are formed by the diagonals.

The top two segments are congruent (blue).

And the bottom two segments are congruent. (brown)

## Example 2

### Example

### Solution

The given quadrilateral is an isosceles trapezoid.

By the diagonals AC and BD,

four segments are formed.

The top two segments are congruent:

AP = BP = 6.

The bottom two segments are congruent:

PD = PC = 11.

See BD.

BP = 6

PD = 11

So BD = 6 + 11.

6 + 11 = 17

So BD = 17.