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.

An isosceles trapezoid is a trapezoid that has congruent legs.

Theorem 6.14 In 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.

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.