2. Kites and Trapezoids 8.5 Chapter 8 Section 8.5 Kites and Trapezoids

3. 8.5 Definition Trapezoid USE PROPERTIES OF KITES AND TRAPEZOIDS A B C D Trapezoid ABCD with Bases

4. Kites and Trapezoids 8.5 Trapezoid Vocabulary USE PROPERTIES OF KITES AND TRAPEZOIDS A B C D Base Angles – Angle formed by a base and a leg Legs – Non-parallel sides Congruent legs make the trapezoid Isosceles Congruent base angles makes the trapezoid Isosceles

5. Kites and Trapezoids 8.5 USE PROPERTIES OF KITES AND TRAPEZOIDS J K L M E F B C D A

6. Kites and Trapezoids 8.5 USE PROPERTIES OF KITES AND TRAPEZOIDS Trapezoid ABCD is Isosceles m  A = m  B = x m  D = m  C = 112 m  A + m  B + m  C + m  D = 360 x + x +112 + 112 = 360 2x + 224 = 360 2x = 136 x = 68

7. Kites and Trapezoids 8.5 USE PROPERTIES OF KITES AND TRAPEZOIDS  A and  D are Supplementary m  A + m  D = 180 m  A + 90 = 180 m  A = 90  B and  C are Supplementary m  B + m  C = 180 132 + m  C = 180 m  C = 48

8. Kites and Trapezoids 8.5 USE PROPERTIES OF KITES AND TRAPEZOIDS Trapezoid ABCD is Isosceles m  A = m  B = x m  D = m  C = 77 m  A + m  B + m  C + m  D = 360 x + x +77 + 77 = 360 2x + 154 = 360 2x = 206 x = 103

9. Kites and Trapezoids 8.5 Theorem USE PROPERTIES OF KITES AND TRAPEZOIDS P Q R S Trapezoid PQSR is Isosceles And Base Angles are   P   Q and  R   S

10. Kites and Trapezoids 8.5 Theorem USE PROPERTIES OF KITES AND TRAPEZOIDS A B C D P Q is a midsegment of Trapezoid ABCD

11. Kites and Trapezoids 8.5 USE PROPERTIES OF KITES AND TRAPEZOIDS The length of the midsegment is equal to half the sum of the bases

12. Kites and Trapezoids 8.5 USE PROPERTIES OF KITES AND TRAPEZOIDS The length of the midsegment is equal to half the sum of the bases

13. Kites and Trapezoids 8.5 USE PROPERTIES OF KITES AND TRAPEZOIDS The length of the midsegment is equal to half the sum of the bases

14. Kites and Trapezoids 8.5 Definition Kite USE PROPERTIES OF KITES AND TRAPEZOIDS Kite GHJK

15. Kites and Trapezoids 8.5 Theorem USE PROPERTIES OF KITES AND TRAPEZOIDS Kite GHJK

16. Kites and Trapezoids 8.5 USE PROPERTIES OF KITES AND TRAPEZOIDS Since the Diagonals are Perpendicular we can use the pythagorean theorem (MA) 2 = 25 + 36 (MA) 2 = 5 2 + 6 2 (MA) 2 = 61 (AT) 2 = 25 + 64 (AT) 2 = 5 2 + 8 2 (AT) 2 = 89

17. Kites and Trapezoids 8.5 Theorem USE PROPERTIES OF KITES AND TRAPEZOIDS Kite GHJK  H   K

18. Kites and Trapezoids 8.5 USE PROPERTIES OF KITES AND TRAPEZOIDS One pair of Opposite angles are congruent m  A = m  H = x m  T = 74, m  M = 27 m  A + m  H + m  M + m  T = 360 x + x + 74 +27 = 360 2x + 101 = 360 2x = 259

19. Kites and Trapezoids 8.5 USE PROPERTIES OF KITES AND TRAPEZOIDS One pair of Opposite angles are congruent m  A = m  H = 118, m  T = x m  A + m  H + m  M + m  T = 360 118 + 118 + 81 + x = 360 x + 317 = 360 x = 43

20. Kites and Trapezoids 8.5 USE PROPERTIES OF KITES AND TRAPEZOIDS 3. Definition   ’s 4. Definition Isosceles Trapezoid

21. Kites and Trapezoids 8.5 USE PROPERTIES OF KITES AND TRAPEZOIDS Quadrialteral with one pair of opp sides || and  base  ’s is isosceles Trapezoid

22. Kites and Trapezoids 8.5 HW #73 Pg 546-547 #1-32