Properties of Trapezoids

Properties of Trapezoids

Leg

Leg

A

B

C

D

Base ›

Base›

Trapezoid

a quadrilateral with exactly one pair of parallel sides.

B

C

D

›

›

Property of a Trapezoid

Leg Angles are Supplementary

A

 A +  C = 180

 B +  D = 180

Isosceles Trapezoid

Definition - A trapezoid with congruent legs.

Properties of Isosceles Trapezoid

• Base Angles Are Congruent
• Diagonals Are Congruent
• Leg Angles are Supplementary

A

B

C

D

Example

Find m P, m Q and mR.

50

S

R

P

Q

Given: m A= 78°, Find  C.

Given: AC = 17.5, AE = 9.6, find BE and BD.

E

Given:

MNOP is an isosceles trapezoid with diagonal PN. m O= 72°, m NPO = 47°, Find m M and m MNP.

JACK is an isosceles trapezoid with diagonal PN. m J= (5x+13)°, m K = (3x-1)°, Find

Given:

m J and m K.

Midsegment

2

Midsegment =

Line that parallel to both bases. Connects the midpoints of the legs. Its length is equal to half of the sum of the length of the bases

b1  b2

Given the figure at the right. ABCD is an Isosceles trapezoid with the midsegment EF. GH is a midsegment of I.T ABFE.

If m D= 74°, AB=34 and CD=26, find EF, GH, m C, m AEF, m BFE, m AGH and

mBHG.

Using Properties of Trapezoids

Find the area of this trapezoid.

Using Properties of Trapezoids

Find the area of a trapezoid with bases of 10 in and 14 in, and a height of 5 in.