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Kites and Trapezoids8.5
Chapter 8Section 8.5
Kites and Trapezoids
Kites and Trapezoids8.5
Definition Trapezoid
USE PROPERTIES OF KITES AND TRAPEZOIDS
A B
C D
Trapezoid ABCD with Bases AB and CD
Kites and Trapezoids8.5
Trapezoid Vocabulary
USE PROPERTIES OF KITES AND TRAPEZOIDS
A B
C DBase Angles – Angle formed by a base and a leg
Legs – Non-parallel sides
Congruent legs make the trapezoid Isosceles
Congruent base angles makes the trapezoid Isosceles
Kites and Trapezoids8.5
USE PROPERTIES OF KITES AND TRAPEZOIDS
J K
LM
E
F
B
C
D
A
Kites and Trapezoids8.5
USE PROPERTIES OF KITES AND TRAPEZOIDS
Trapezoid ABCD is Isosceles
mA = mB = x mD = mC = 112
mA + mB + mC + mD = 360
x + x +112 + 112 = 360
2x + 224 = 360
2x = 136
x = 68
Kites and Trapezoids8.5
USE PROPERTIES OF KITES AND TRAPEZOIDS
A and D are Supplementary
mA + mD = 180
mA + 90 = 180
mA = 90
B and C are Supplementary
mB + mC = 180
132 + mC = 180
mC = 48
Kites and Trapezoids8.5
USE PROPERTIES OF KITES AND TRAPEZOIDS
Trapezoid ABCD is Isosceles
mA = mB = x mD = mC = 77
mA + mB + mC + mD = 360
x + x +77 + 77 = 360
2x + 154 = 360
2x = 206
x = 103
Kites and Trapezoids8.5
Theorem
USE PROPERTIES OF KITES AND TRAPEZOIDS
P Q
R SQR PS Trapezoid PQSR is Isosceles
And
Base Angles are P Q and R S
Kites and Trapezoids8.5
Theorem
USE PROPERTIES OF KITES AND TRAPEZOIDS
A B
C D
P Q
is a midsegment of Trapezoid ABCDPQ
CDPQandABPQ ||||
)(21
CDABPQ
Kites and Trapezoids8.5
USE PROPERTIES OF KITES AND TRAPEZOIDS
The length of the midsegment is equal to half the sum of the bases
)147(21
RT
21
10221
RT
Kites and Trapezoids8.5
USE PROPERTIES OF KITES AND TRAPEZOIDS
The length of the midsegment is equal to half the sum of the bases
)x8(21
11
x822
x14
Kites and Trapezoids8.5
USE PROPERTIES OF KITES AND TRAPEZOIDS
The length of the midsegment is equal to half the sum of the bases
)24x(21
13
24x26
x2
Kites and Trapezoids8.5
Definition Kite
USE PROPERTIES OF KITES AND TRAPEZOIDS
Kite GHJK
Kites and Trapezoids8.5
Theorem
USE PROPERTIES OF KITES AND TRAPEZOIDS
GJ HKKite GHJK
Kites and Trapezoids8.5
USE PROPERTIES OF KITES AND TRAPEZOIDS
Since the Diagonals are Perpendicular we can use the pythagorean theorem
(MA)2 = 25 + 36
(MA)2 = 52 + 62
(MA)2 = 61(AT)2 = 25 + 64
(AT)2 = 52 + 82
(AT)2 = 8961MA
61MH 89AT
89TH
Kites and Trapezoids8.5
Theorem
USE PROPERTIES OF KITES AND TRAPEZOIDS
Kite GHJK H K
Kites and Trapezoids8.5
USE PROPERTIES OF KITES AND TRAPEZOIDS
One pair of Opposite angles are congruent
mA = mH = x
mT = 74, mM = 27
mA + mH + mM + mT = 360
x + x + 74 +27 = 360
2x + 101 = 360
2x = 259
21
1292
259x
Kites and Trapezoids8.5
USE PROPERTIES OF KITES AND TRAPEZOIDS
One pair of Opposite angles are congruent
mA = mH = 118, mT = x
mA + mH + mM + mT = 360
118 + 118 + 81 + x = 360
x + 317 = 360
x = 43
Kites and Trapezoids8.5
USE PROPERTIES OF KITES AND TRAPEZOIDS
3. Definition ’s4. Definition Isosceles Trapezoid
Kites and Trapezoids8.5
USE PROPERTIES OF KITES AND TRAPEZOIDS
Quadrialteral with one pair of opp sides || and base ’s is isosceles Trapezoid
Kites and Trapezoids8.5
HW #73Pg 546-547 #1-32
