# Properties of an Isosceles Trapezoid

How to solve the isosceles trapezoid problems by using its properties: definition, properties of its angles and diagonals, examples, and their solutions.

## 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.

Properties of a trapezoid

## Property: Angles

There are two properties

of the angles of an isosceles trapezoid.

1. The upper base angles are congruent.

And the lower base angles are congruent.

2. Two interior angles that inscribe the leg

are supplementary:

m∠[blue] + m∠[green] = 180

Supplementary angles

This is true because

these two angles are

the consecutive interior angles in parallel lines.

Consecutive interior angles in parallel lines

## Example 1

∠*A* and ∠*D* are the angles

that inscribe the same leg.

m∠*D* = 60

So m∠*A* + 60 = 180.

Move +60 to the right side.

Then m∠*A* = 120.

∠*A* and ∠*B* are the upper base angles.

m∠*A* = 120

So m∠*B* = 120.

∠*D* and ∠*C* are the lower base angles.

m∠*D* = 60

So m∠*C* = 60.

So m∠*A* = 120, m∠*B* = 120, and m∠*C* = 60.

## Property: Diagonals

For the segments

formed by the diagonals of an iscosceles trapezoid,

the upper segments are congruent,

and the lower segments are congruent.

## Example 2

The given figure is an isosceles trapezoid.

So the upper segments

formed by the diagonals

are congruent.

So the upper right segment is 6.

For *BD*,

the upper segment is 6

and the lower segment is 11.

So *BD* = 6 + 11

= 17.