6.6 Trapezoids and Kites • A

trapezoid

is a quadrilateral with exactly one pair of parallel sides. • The parallel sides of a trapezoid are called

bases

.

• The nonparallel sides are called

legs

.

• Two angles that share a base of a trapezoid are called

base angles

.

• An

isosceles trapezoid

is a trapezoid with legs that are congruent.

Theorem 6.19

• If a quadrilateral is an isosceles trapezoid, then each pair of base angles is congruent.

Finding Angle Measures in Trapezoids • CDEF is an isosceles trapezoid and the measure of angle C = 65. What are the measures of angle D, angle E, and angle F?

65 180 115 180

m F m E

65 115

Theorem 6.20

• If a quadrilateral is an isosceles trapezoid, then its diagonals are congruent.

Midsegment of a Trapezoid

• The

midsegment of a trapezoid

that joins the midpoints of its legs.

is the segment – Is parallel to the bases.

– The length of the midsegment is half the sum of the lengths of the bases.

Kites

• A

kite

is a quadrilateral with two pairs of consecutive sides congruent and no opposite sides congruent.

Theorem 6.22

• If a quadrilateral is a kite, then its diagonals are perpendicular.

Finding Angle Measures in Kites

• Quadrilateral DEFG is a kite. What are the measures of angle 1, angle 2, and angle 3?

m

1 90 90 142

m m

180

m

2

m

3 38 52

Concept Summary

More Practice!!!!!

• Homework – Textbook p. 394 – 395 #7 – 36 ALL.