6.6 Trapezoids and Kites

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?

180m C m D 65 180m D

115m D

65

115

m C m F

m D m E

Theorem 6.20

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

Midsegment of a Trapezoid

• The midsegment of a trapezoid is the segment that joins the midpoints of its legs.– 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?

1 90m

90 2 52 180m 142 2 180m

2 38m

3 52m

Concept Summary

More Practice!!!!!

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