1. What are Kites?

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

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

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

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

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

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

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

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

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

11. 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 )

12. Find the measures of the angles in trapezoid48
m< A = 132
m< B = 132
m< D = 48

13. Find BE
AC = 17.5, AE = 9.6 E

14. Example
Find the side lengths of the kite.

15. Example 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

16. Find the lengths of the sides of the kiteW 4 Z X 5 5 8 Y

17. Find the lengths of the sides of kite to the nearest tenth2 4 7 2

18. 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

19. 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

20. 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

21. Using Properties of Trapezoids
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.
Area of trapezoid =
Find the area of this trapezoid.
A = ½ * 26 * ( )
A = 806

22. 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.

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

24. a) Find the lengths of all the sides.
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.

25. Venn Diagram:
– Properties of Parallelograms

26. Flow Chart: