Trapezoid: Property

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

Definition

Definition

A trapezoid is a quadrilateral
that have a pair of parallel sides.

Base: Parallel sides
Legs: Non-parallel sides

Property: Angles

Property

For a trapezoid,
two interior angles that inscribe the same leg
are supplementary.

m∠1 + m∠2 = 180
m∠1' + m∠2' = 180

Example 1

Example

Solution

The given quadrilateral is a trapezoid.

These two angles inscribe the same left leg.

So [x + 40] + [60] = 180.

+40 + 60 = +100

Move +100 to the right side.

Then x = 80.

Next, these two angles inscribe the same right leg.

So [8y] + [108] = 180.

Move +108 to the right side.

Then 8y = 72.

Divide both sides by 8.

Then y = 9.

x = 80
y = 9

Write these below.

So
x = 80
y = 9
is the answer.

Property: Median

Definition

The median of a trapezoid
is a line segment
that connects the midpoints of the legs.

It's like the midsegment of a triangle.

Property

The median has two properties.

The median and the bases are parallel.

The median (m) and the bases (b1, b2)
satisfy this formula:
m = [1/2](b1 + b2).

Example 2

Example

Solution

The given quadrilateral is a trapezoid.

The blue segment connects
the midpoints of two legs.

So the blue segment is the median.

The median is x.
The bases are 3 and 7.

So x = [1/2](3 + 7).

(3 + 7) = 10

10/2 = 5

So x = 5.