Lesson 5.3 Trapezoids and Kites Homework: 5.3/1-8,19 QUIZ Wednesday 5.1 – 5.4 PROCEDURES for today: 1. OPEN TEXTBOOKS 2. Tools – patty paper(2), protractor, ruler 3. INVESTIGATIONs 1 & 2 – ALL steps 4. Complete the 4 kite conjectures & the 3 trapezoid conjectures 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. C B D A AC BD Non-Vertex Angles of a Kite If a quadrilateral is a kite, then nonvertex angles are congruent C D B A A C, B D Vertex diagonals bisect vertex angles If a quadrilateral is a kite then the vertex diagonal bisects the vertex angles. C B D A Vertex diagonal bisects the non-vertex diagonal If a quadrilateral is a kite then the vertex diagonal bisects the non-vertex diagonal C B D A Trapezoid Definition-a quadrilateral with exactly one pair of parallel sides. A Base › B Leg Leg C › Base D Property of a Trapezoid Leg Angles are Supplementary A › B <A + <C = 180 <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 S R 50 P Q PQRS is an isosceles trapezoid. Find m P, m Q and mR. m R = 50 since base angles are congruent mP = 130 and mQ = 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. X 12 W 20 12 U 12 Z Y Example Continued X 12 W 20 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 WX = 4 34 XY =12 2 likewise WZ = 4 34 likewise ZY =12 2 12 U 12 Z Y 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 J Find mG and mJ. H 132 Since GHJK is a kite G J So 2(mG) + 132 + 60 = 360 2(mG) =168 mG = 84 and mJ = 84 G 60 K Try This! RSTU is a kite. Find mR, mS and mT. S R x+30 x T 125 U x +30 + 125 + 125 + x = 360 2x + 280 = 360 2x = 80 x = 40 So mR = 70, mT = 40 and mS = 125 Try These 2. m<C = x +12 and m<B = 3x – 2, find x and the measures of the 2 angles 1. If <A = 134, find m<D A base leg D base m<D = 46 A B leg leg C D base B leg base x = 42.5 m<C = 54.5 m<B = 125.5 C Using Properties of Trapezoids When working with a trapezoid, the height may be measured anywhere between the two bases. Also, beware of "extra" information. The 35 and 28 are not needed to compute this area. 1 Area of trapezoid = hb1 b2 2 Find the area of this trapezoid. A = ½ * 26 * (20 + 42) A = 806 Using Properties of Trapezoids Example 2 Find the area of a trapezoid with bases of 10 in and 14 in, and a height of 5 in. Using Properties of Kites Area Kite = one-half product of diagonals 1 A d1d 2 2 D 1 Area AC BD 2 A B C Using Properties of Kites Example 6 ABCD is a Kite. A a) Find the lengths of all the sides. D 2 E 4 4 4 b) Find the area of the Kite. C B Venn Diagram: http://teachers2.wcs.edu/high/rhs/staceyh/Geometry/Chapter%206%20Notes.ppt#435,22,6.2 – Properties of Parallelograms Flow Chart: Homework