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GEOMETRY WARM UPS #5
6-6 TRAPEZOIDS AND KITES
TRAPEZOID

Quadrilateral with one pair of parallel sides
Parallel sides are called the “bases”.
 Non-parallel sides are called the “legs”.

ISOSCELES TRAPEZOID

Trapezoid where the legs are congruent

Diagonals are congruent.
THEOREM

Base angles of an isosceles trapezoid are
congruent.
y
x

y
x
What else can you tell me about angles x and y?

They are supplements!
TOO: FIND THE MISSING ANGLES
1)
110
110
70
2)
35
70
145
145
35
THEOREM
midsegment

The median of a trapezoid is
parallel to the bases
 (Base + Base) divided by 2

b
m
b
bb
m
2
midsegment
EXAMPLE: EF IS THE MEDIAN OF
base  base
TRAPEZOID ABCD
midsegment 
2
1)
2)
25  13
EF 
2
29  DC
24 
2
If AB = 25 and DC = 13, find EF. 19
If AB = 29 and EF = 24, find DC. 19
D
C
E
F
A
B
TOO: If AB = 7y + 6, EF = 5y – 3, and DC = y – 5,
find y and EF. (both answers are decimals!!)
3.5 14.5
7y  6 y 5
5y  3 
2
Kite

Is a Quadrilateral
Diagonals are Perpendicular
 2 consecutive sets of sides
are congruent
 Longer diagonal bisects the
angles and the shorter diagonal.

EXAMPLE
If BCDE is a kite, find mE and mD.
130
36
36
130
64+130+130+___ = 360
324+___ = 360
___ = 360 – 324
___ = 36
TOO: KITE CDEF
If m∠DCF = 48 and m∠DEF = 88,
 find m∠CDE and m∠DCR

112
24
360-88-48= 224
112
Divide 224 by 2
88
224 / 2 = 112
112
48
Divide: 48 / 2 = 24
HOMEWORK
Pg.
394-395 #7-23 odd, 29-35 odd