Trapezoids

Definition of a Trapezoid

1. A trapezoid is a quadrilateral with two and only two parallel sides

2. The parallel sides are called the bases

3. The nonparallel sides are called the legs

Bases

Legs

Trapezoid

Isosceles Trapezoids1. An isosceles trapezoid is a trapezoid in

which the two nonparallel sides are congruent

2. Isosceles Trapezoid Theorems:1. If a trapezoid is isosceles, then the base

angles are congruent.2. If the base angles of a trapezoid are

congruent then the trapezoid is isosceles3. If a trapezoid is isosceles, then the diagonals

are congruent4. If the diagonals of a trapezoid are congruent,

then the trapezoid is isosceles

A B

D C A B

AB BDAD BC

Median of a Trapezoid1. The median of a trapezoid is a line

segment whose endpoints are the midpoints of the nonparallel sides of the trapezoid.

2. Trapezoid Median Theorems:1. The median of a trapezoid is parallel to the

bases.2. The length of a median of a trapezoid is equal

to one-half the sum of the bases.

A B

D C

M N

2

AB DCMN

Useful Equations

2 1 2 1,2 2

x x y y

Midpoint

Point slope formula:y b

mx a

2 1

2 1

slopeof a liney y

AB mx x

*+++++++++++++ +

Trapezoid Example• Given the Polygon described by: A(-2, -5), B(8,5), C(4,5),

D(-2, -1) show:

The length of the median is ½ the sumof the bases

ABCD is a trapezoidABCD is isoscelesThe median isparallel to the bases