8.5 Trapezoids

Trapezoids

You will learn to identify and use the properties of trapezoidsand isosceles trapezoids.

1) Trapezoid

Trapezoids

A trapezoid is a ____________ with exactly one pair of ____________.quadrilateral parallel sides

T

P A

R

The parallel sides are called ______.bases

base

baseThe non parallel sides are called _____.legs

leg leg

Each trapezoid has two pair ofbase angles.

base anglesT and R are one pairof base angles.

P and A are the other pair of base angles.

Trapezoids

Theorem8-13

The median of a trapezoid is parallel to the _____, basesand the length of the median equals _______________ of the lengths of the bases.

one-half the sum

C

N

B

D

M

A

MNDCMNAB || ,||

DCABMN 2

1

Trapezoids

C

N

D

M

BA

Find the length of median MN in trapezoid ABCD if AB = 16 and DC = 20

16

20

DCABMN 2

1

20162

1MN

362

1MN

18MN

18

Trapezoids

If the legs of a trapezoid are congruent, the trapezoid is an _________________.isosceles trapezoid

In lesson 6 – 4, you learned that the base angles of an isosceles triangle arecongruent.

There is a similar property of isosceles trapezoids.

Trapezoids

Theorem8-14

Each pair of __________ in an isosceles trapezoid is congruent.base angles

Z Y

XW

XW

YZ

Trapezoids

T

P A

R

60°

Find the missing angle measures in isosceles trapezoid TRAP.

P A

mP = mA

60 = mA

60°

Theorem 8 – 14

T R

P + A + 2(T) = 360

Theorem 8 – 14

60 + 60 + 2(T) = 360

120 + 2(T) = 360

2(T) = 240

T = 120

120°

R = 120

120°

Trapezoids