# 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 (b_{1}, b_{2})

satisfy this formula:

m = [1/2](b_{1} + b_{2}).

## 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.