1. Lesson 5.3 Trapezoids and Kites
Homework: 5.3/1-8,19
QUIZ Wednesday 5.1 – 5.4

2. PROCEDURES for today:
1. OPEN TEXTBOOKS 2. Tools – patty paper(2), protractor, ruler 3. INVESTIGATIONs 1 & 2 – ALL steps 4. Complete the 4 kite conjectures & the 3 trapezoid conjectures

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

4. Parts of a Kite Vertex angles: <B & <D Vertex diagonal BD
Non-Vertex diagonal CA
Non-Vertex angles: <A & <C

5. Properties of Kites The diagonals of a kite are perpendicular
Non-vertex angles (a)are congruent
Vertex diagonal bisects the
vertex angles
non-vertex diagonal

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

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

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

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

10. 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

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

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

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

14. 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 )

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

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

17. Example
Find the side lengths of the kite.

18. 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

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

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

21. 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

22. 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

25. 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

26. 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

27. 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.

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

32. 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.

33. Venn Diagram:
– Properties of Parallelograms

34. Flow Chart:

35. Homework