Lesson 5.3 Trapezoids and Kites

1. Lesson 5.3Trapezoids and Kites Homework: 5.3/1-8,19 QUIZ Wednesday 5.1 – 5.4

2. PROCEDURES for today: 1. OPEN TEXTBOOKS2. Tools – patty paper(2), protractor, ruler3. INVESTIGATIONs 1 & 2 – ALL steps4. Complete the 4 kite conjectures & the 3 trapezoid conjectures

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

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

5. A C, B D Non-Vertex Angles of a Kite • If a quadrilateral is a kite, then non-vertex angles are congruent

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

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

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

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

10. Isosceles Trapezoid Definition - A trapezoid with congruent legs.

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

12. Example PQRS is an isosceles trapezoid. Find m P, m Q and mR. 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 )

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

14. Find BE • AC = 17.5, AE = 9.6 E

15. Example • Find the side lengths of the kite.

16. Example Continued 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

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

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

19. 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

20. 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 mR = 70, mT = 40 and mS = 125

23. 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 x = 42.5 m<C = 54.5 m<B = 125.5 m<D = 46

24. Using Properties of Trapezoids Area of trapezoid = 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. Find the area of this trapezoid. A = ½ * 26 * (20 + 42) A = 806

25. 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.

29. Using Properties of Kites Area Kite = one-half product of diagonals

30. Using Properties of Kites Example 6 ABCD is a Kite. a) Find the lengths of all the sides. 2 4 4 E 4 • Find the area of the Kite.

31. Venn Diagram: http://teachers2.wcs.edu/high/rhs/staceyh/Geometry/Chapter%206%20Notes.ppt#435,22,6.2 – Properties of Parallelograms

32. Flow Chart:

33. Homework