1. Trapezoids and Kites

2. Essential Questions How do I use properties of trapezoids?
How do I use properties of kites?

3. Vocabulary
Trapezoid – a quadrilateral with exactly one pair of parallel sides.
A trapezoid has two pairs of base angles. In this example the base angles are A & B and C & D
leg
base

4. Base Angles Trapezoid Theorem
If a trapezoid is isosceles, then each pair of base angles is congruent.
 A   B,  C   D

5. Base Angles Trapezoid Converse
If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid.
ABCD is an isosceles trapezoid

6. Diagonals of a Trapezoid Theorem
A trapezoid is isosceles if and only if its diagonals are congruent.

7. Example 1 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 )

8. Definition
Midsegment of a trapezoid – the segment that connects the midpoints of the legs.

9. Midsegment Theorem for Trapezoids
The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases.

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

11. Theorem: Perpendicular Diagonals of a Kite
If a quadrilateral is a kite, then its diagonals are perpendicular.

12. Theorem: Opposite Angles of a Kite
If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent
A  C, B  D

13. Example 2
Find the side lengths of the kite.

14. Example 2 Continued
We can use the Pythagorean Theorem to find the side lengths.
= (WX)2
= (WX)2
544 = (WX)2
= (XY)2
= (XY)2
288 = (XY)2

15. 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

16. Try This! RSTU is a kite. Find mR, mS and mT.
x x = 360
2x = 360
2x = 80
x = 40
So mR = 70, mT = 40 and mS = 125

17. Homework
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2- 14 evens
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6 – 12 all