Properties of an Isosceles Trapezoid

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. Its base angles are also congruent.

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

The upper base angles are congruent. And the lower base angles are congruent. Two interior angles that inscribe the leg are supplementary.

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

Find the measure of angle A, B, and C. The measure of angle D: 60.

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.

For the segments
formed by the diagonals of an iscosceles trapezoid,

the upper segments are congruent,
and the lower segments are congruent.

Example 2

Find BD. Upper left segment: 6, lower left segment: 11

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.