Geometry Section 6.5

Trapezoids and Kites

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

The sides that are parallel are called _______.

The nonparallel sides are called ______.

The angles at each end of a base are called _____________.

bases

legs

base angles

Note: Since a trapezoid has only one pair of opposite sides parallel,

it is not a parallelogram and will not have the properties of a

parallelogram.

A midsegment of a trapezoid is the segment joining the midpoints of

the two legs.

Theorem 6.17 The midsegment of a trapezoid is parallel

to the bases and the length of the midsegment is equal to ½ the sum of the

bases.

FCEDAB ////

EDABFC

EDABFC

221

An isosceles trapezoid is a trapezoid that has congruent legs.

Theorem 6.14In an isosceles trapezoid, the base angles that share a common base are congruent.

Note: For any trapezoid the angles that share a common leg are _____________.supplementary

Theorem 6.16

In an isosceles trapezoid, the diagonals are congruent.

Example 1: Find the value of x, y and z in this isosceles trapezoid.

43y137z

25.16885

8568

47123880

318164)1940(2

x

x

xx

xxx

A kite is a quadrilateral with two pairs of congruent adjacent sides and noncongruent opposite sides.

Theorem 6.18

In a kite, the diagonals are perpendicular.

Example 2: Find the perimeter of the kite.

222 5.1318 c5.22c

222 4.325.13 c1.35c

2.115)1.35(2)5.22(2 P