Lesson 6 6 Trapezoids and Kites Definition Kite

Lesson 6. 6 Trapezoids and Kites

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

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

Non-Vertex Angles of a Kite If a quadrilateral is a kite, then nonvertex angles are congruent A C, B D

Vertex diagonals bisect vertex angles If a quadrilateral is a kite then the vertex diagonal bisects the vertex angles.

Vertex diagonal bisects the non-vertex diagonal If a quadrilateral is a kite then the vertex diagonal bisects the non-vertex diagonal

Trapezoid Definition-a quadrilateral with exactly one pair of parallel sides. A Base › B Leg C › Base D

Property of a Trapezoid Leg Angles are Supplementary A <A + <C = 180 › B <B + <D = 180 C › D

Isosceles Trapezoid Definition - A trapezoid with congruent legs.

| | Isosceles Trapezoid - Properties 1) Base Angles Are Congruent 2) Diagonals Are Congruent

Example PQRS is an isosceles trapezoid. Find m P, m Q and m R = 50 since base angles are congruent m P = 130 and m Q = 130 (consecutive angles of parallel lines cut by a transversal are )

Find the measures of the angles in trapezoid 48 m< A = 132 m< B = 132 m< D = 48

Find BE AC = 17. 5, AE = 9. 6 E

Example Find the side lengths of the kite.

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

Find the lengths of the sides of the kite W 4 Z 5 5 8 Y X

Find the lengths of the sides of kite to the nearest tenth 2 4 7 2

Example 3 Find m G and m J. Since GHJK is a kite G J So 2(m G) + 132 + 60 = 360 2(m G) =168 m G = 84 and m J = 84

Try This! RSTU is a kite. Find m R, m S and m T. x +30 + 125 + x = 360 2 x + 280 = 360 2 x = 80 x = 40 So m R = 70 , m T = 40 and m S = 125