1. 6.6 Trapezoids & Kites

2. Trapezoid ( Old Regular)
Trapezoid: Is a quadrilateral with exactly one pair of parallel sides. *The parallel sides are the bases. *The nonparallel sides are the legs.
Base
Leg
Base 

3. In the Old Regular Two rules
#1 Consecutive angles between the parallel lines are supplementary (add to 180°)
#2 All angles add to 360°

4. Special trapezoid Isosceles Trapezoid has equal legs
If the legs of the trapezoid are congruent then it is an isosceles trapezoid.

5. Isosceles Trapezoid: Rule #1
If a Trapezoid is isosceles, then each pair of base angles are congruent. B A C D
A  B & C  D

6. Isosceles Trapezoid: Rule #2
If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid. B A C D
ABCD is an isosceles trapezoid

7. Isosceles Trapezoid: Rule #3
A trapezoid is isosceles if and only if its diagonals are congruent. B A C D
ABCD is isosceles if and only if

8. Midsegment of Iso Trapezoid
Midsegment: of a Isoceles trapezoid is the segment that connects the midpoints of its legs. All segments congruent B A C D M N
Midsegment

9. Midsegment in old regularB A C D M N
Midsegment

10. Midsegment Theorem of Trapezoid
The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases. B A C D M N
MNAB, MNDC, MN =

11. Example #1
Find length MN B A C D M N 12 9

12. Example #2
Find the length of AB B A C D M N 20 10

13. Example #3
Find the length of DC B A C D M N 15 25

14. Kite
Kite: is a quadrilateral that the two pairs of consecutive congruent sides, but opposite sides are not congruent.

15. Kite: Rule #1
If a quadrilateral is a kite, then its diagonals are perpendicular.
KM  JL

16. Kite: Rule #2
If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.
JKL  JML
KJM  KLM

17. Kite: Rule #3
If a quadrilateral is a kite, the non-congruent angles are bisected by diagonal.

18. Homework 6.6