Trapezoids

1. Properties of Trapezoids

2. a quadrilateral with exactly one pair of
parallel sides.
Leg Leg
Base
Base
A B
C D›
›
Trapezoid

3. A B
C D
›
›
Leg Angles are Supplementary
Property of a Trapezoid
 A +  C = 180
 B +  D = 180

4. Isosceles Trapezoid
Definition - A trapezoid with congruent legs.

5. Properties of Isosceles Trapezoid
1) Base Angles Are Congruent
2) Diagonals Are Congruent
3) Leg Angles are Supplementary
A B
C D

6. Example
Find m P, m Q and
mR.
50
S R
P Q

7. Given: m A= 78°, Find
 C.

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

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

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

11. Midsegment
2
21 bb 
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

12. 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.

13. Using Properties of Trapezoids
Find the area of this trapezoid.

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