7.4 Trapezoids and Kites Objectives: • Definitions of trapezoid and kite. • Properties of trapezoids and kites.

Concept: Diagonals of a Trapezoid Theorem A trapezoid is isosceles if and only if its diagonals are congruent.

Example 1 PQRS is an isosceles trapezoid. Find mLP, mLQ and mLR. MLR = 50º since base angles are congruent mLP = 130º and mLQ = 130º

Concept: Definition of Kite Kite – a quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent.

Concept: Vertex Angles Vertex angles: Angles formed between the two congruent sides. Vertex angles

Concept: Non-Vertex Angles Non-Vertex angles: Angles formed between the two non-congruent sides. Non-vertex angles are congruent, Non-Vertex angles

Concept: Perpendicular Diagonals of a Kite If a quadrilateral is a kite, then its diagonals are perpendicular.

Concept: Opposite Angles of a Kite If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent LA = LC, LB ≠ LD

Example 2 Find the side lengths of the kite.

Example 2 Cont… We can use the Pythagorean Theorem to find the side lengths. 122 + 202 = (WX)2 144 + 400 = (WX)2 544 = (WX)2 122 + 122 = (XY)2 144 + 144 = (XY)2 288 = (XY)2

Example 3 Find mLG and mLJ. Since GHJK is a kite, LG = LJ So 2(mLG) + 132º + 60º = 360º 2(mLG) =168º mLG = 84º and mLJ =84º

Concept: Try This! RSTU is a kite. Find mR, mS and mT. x +30 + 125 + 125 + x = 360 2x + 280 = 360 2x = 80 x = 40 So mLR = 70º, mLT = 40º and mLS = 125º

Homework Practice Master 7.4