1. 8.5 – Use Properties of Trapezoids and Kites

2. Trapezoid: Consecutive interior angles are supplementary A B C D m  A + m  D = 180° m  B + m  C = 180° Quadrilateral with one pair of opposite sides parallel base leg

3. Isosceles Trapezoid: The nonparallel sides of the trapezoid are congruent

4. Isosceles Trapezoid: The base angles are congruent The diagonals are congruent A B CD

5. Midsegment of a Trapezoid: The midsegment is half the sum of the parallel sides A B CD F E

6. Kite: Quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent

7. Kite: Exactly one pair of opposite angles are  Its diagonals are perpendicular

8. Find the m  B, m  C, m  D. 53° m  B = 53° 180-53 = m  C = 127° m  D =

9. Find the m  B, m  C, m  D. 180-97 = m  B = m  C = 83° 97° m  D = 83°

10. Find the length of the midsegment.

12. Find x. 8 = 4x 2 = x 1

13. Find x. x = 4 1 7x = 28

14. Given the isosceles trapezoid, find x and all base angles. 1 80° 100°

15. Determine whether the quadrilateral is a trapezoid. If it is, is it an isosceles trapezoid? Yes, it is a trapezoid Alternate interior angles are , so one pair of parallel lines No

16. Determine whether the quadrilateral is a trapezoid. If it is, is it an isosceles trapezoid? No, No parallel lines

17. Determine whether the quadrilateral is a trapezoid. If it is, is it an isosceles trapezoid? Yes, Base angles are congruent Isosceles trapezoid

18. WEST is a kite. Find the missing angles. 29 + x + 95 + x = 360 2x + 124 = 360 2x = 236 x = 118° x x

19. WEST is a kite. Find the missing angles. x 107 + 88 + x + 88 = 360 x + 283 = 360 x = 77° 88°

20. HW Problem 8.5546-5481, 8-11, 13, 15, 19-21, 25-29 odd #20, SKIP # 21 Ans: x + x + 150 + 90 = 360 x = 60° xx