Section 6-5 Trapezoids and Kites

Trapezoid A quadrilateral with exactly one pair of parallel sides.

The parallel sides are called the bases. The nonparallel sides are called the legs. A trapezoid has two pairs of base angles.

Base leg A B C D Base Angles: and

Isosceles Trapezoid A trapezoid whose legs are congruent.

Theorem 6-14 If a trapezoid is isosceles, then each pair of base angles is congruent. A B C D Therefore

Theorem 6-15 If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid. A B C D is an isosceles trapezoid. Therefore

Theorem 6-16 A trapezoid is isosceles if and only if its diagonals are congruent. A B C D is isosceles Therefore

MIDSEGMENT of a trapezoid The segment that connects the midpoints of its legs. Midsegment A C B D

Theorem 6-17 The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases.

A C B D ║ ║ N M