6.2.3 Properties of Kites and Trapezoids Key Objectives • Use properties of kites to solve problems. • Use properties of trapezoids to solve problems. Key Terms • A kite is a quadrilateral with exactly two pairs of congruent consecutive sides. • A trapezoid is a quadrilateral with exactly one pair of parallel sides. • Each of the parallel sides of a trapezoid is called a base of a trapezoid . • The nonparallel sides of a trapezoid are called legs . • Base angles of a trapezoid are two consecutive angles whose common side is a base. • If the legs of a trapezoid are congruent, the trapezoid is an isosceles trapezoid . • The midsegment of a trapezoid is the segment whose endpoints are the midpoints of the legs. Theorems, Postulates, Corollaries, and Properties • Theorem If a quadrilateral is a kite, then its diagonals are perpendicular. • Theorem If a quadrilateral is a kite, then exactly one pair of opposite angles is congruent. • Theorem If a quadrilateral is an isosceles trapezoid, then each pair of base angles is congruent. • Theorem If a trapezoid has one pair of congruent base angles, then the trapezoid is isosceles. • Theorem A trapezoid is isosceles if and only if its diagonals are congruent. • Theorem The midsegment of a trapezoid is parallel to each base, and its length is one-half the sum of the lengths of the bases. Example 1 Problem-Solving Application This is a property of kites. If a quadrilateral is a kite, then its diagonals are perpendicular.
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