1. Chapter 6 Section 6.5B
Kites and Trapezoids

2. Trapezoid ABCD with Bases
USE PROPERTIES OF KITES AND TRAPEZOIDS
Definition Trapezoid A B C D
Trapezoid ABCD with Bases

3. Legs – Non-parallel sides Congruent legs make the trapezoid Isosceles
USE PROPERTIES OF KITES AND TRAPEZOIDS
Trapezoid Vocabulary
Legs – Non-parallel sides
Congruent legs make the trapezoid Isosceles A B C D
Base Angles – Angle formed by a base and a leg
Congruent base angles makes the trapezoid Isosceles

4. USE PROPERTIES OF KITES AND TRAPEZOIDSM L J K E B D F C A

5. Trapezoid ABCD is Isosceles
USE PROPERTIES OF KITES AND TRAPEZOIDS
Trapezoid ABCD is Isosceles
mA = mB = x
mD = mC = 112
mA + mB + mC + mD = 360
x + x = 360
2x = 360
2x = 136
x = 68

6. A and D are Supplementary mA + mD = 180 mA + 90 = 180 mA = 90
USE PROPERTIES OF KITES AND TRAPEZOIDS
A and D are Supplementary
mA + mD = 180
mA + 90 = 180
mA = 90
B and C are Supplementary
mB + mC = 180
132 + mC = 180
mC = 48

7. Trapezoid ABCD is Isosceles
USE PROPERTIES OF KITES AND TRAPEZOIDS
Trapezoid ABCD is Isosceles
mA = mB = x
mD = mC = 77
mA + mB + mC + mD = 360
x + x = 360
2x = 360
2x = 206
x = 103

8. Trapezoid PQSR is Isosceles And Base Angles are  P  Q and R  S
USE PROPERTIES OF KITES AND TRAPEZOIDS
Theorem P Q R S
Trapezoid PQSR is Isosceles
And
Base Angles are  P  Q and R  S

9. is a midsegment of Trapezoid ABCD A B
USE PROPERTIES OF KITES AND TRAPEZOIDS
Theorem
is a midsegment of Trapezoid ABCD A B C D P Q

10. The length of the midsegment is equal to half the sum of the bases
USE PROPERTIES OF KITES AND TRAPEZOIDS
The length of the midsegment is equal to half the sum of the bases

11. The length of the midsegment is equal to half the sum of the bases
USE PROPERTIES OF KITES AND TRAPEZOIDS
The length of the midsegment is equal to half the sum of the bases

12. The length of the midsegment is equal to half the sum of the bases
USE PROPERTIES OF KITES AND TRAPEZOIDS
The length of the midsegment is equal to half the sum of the bases

13. USE PROPERTIES OF KITES AND TRAPEZOIDS
Definition Kite
Kite GHJK

14. USE PROPERTIES OF KITES AND TRAPEZOIDS
Theorem
Kite GHJK

15. USE PROPERTIES OF KITES AND TRAPEZOIDS
Since the Diagonals are Perpendicular we can use the pythagorean theorem
(MA)2 =
(AT)2 =
(MA)2 =
(AT)2 =
(MA)2 = 61
(AT)2 = 89

16. USE PROPERTIES OF KITES AND TRAPEZOIDS
Theorem
H  K
Kite GHJK

17. One pair of Opposite angles are congruent
USE PROPERTIES OF KITES AND TRAPEZOIDS
mA = mH = x
mT = 74, mM = 27
mA + mH + mM + mT = 360
x + x = 360
2x = 360
2x = 259
One pair of Opposite angles are congruent

18. One pair of Opposite angles are congruent
USE PROPERTIES OF KITES AND TRAPEZOIDS
One pair of Opposite angles are congruent
mA = mH = 118, mT = x
mA + mH + mM + mT = 360
x = 360
x = 360
x = 43

19. 4. Definition Isosceles Trapezoid
USE PROPERTIES OF KITES AND TRAPEZOIDS
3. Definition  ’s
4. Definition Isosceles Trapezoid

20. USE PROPERTIES OF KITES AND TRAPEZOIDS
Quadrialteral with one pair of opp sides || and  base ’s is isosceles Trapezoid

21. HW #73 Pg Odd, Odd, 47, 49, Even