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CP Geometry
Mr. Gallo
What is a Trapezoid
If a quadrilateral is a trapezoid, then
_________________
it has exactly
_______________________.
one pair of parallel sides
Trapezoid
A
leg
D
Base
B
Base Angles
leg
C
Base
Isosceles Trapezoid
A
The legs in an isosceles
trapezoid are
congruent.
leg
D
Base
Base Angles
Base
B
leg
C
Theorem 6-19
If a quadrilateral is an isosceles trapezoid,
_______________________________________.
then each pair of base angles is congruent
A
D
B
C
Then the following angles are congruent:
D  
____
A  ____
C
B
Complete Got It? #1 p. 390
a. 𝑚∠𝑃 = 𝑚∠𝑄 = 74°, 𝑚∠𝑆 = 106°
b. Yes; 𝐷𝐸 ∥ 𝐶𝐹 so SSI angles are supplementary.
What are the values of x and y in the isosceles
triangle below if 𝐷𝐸 is a midsegment?
B
y
D
x
A
32
180  32
mB  y 
 74
2
E
C
mBDE  x  180  74  106
Theorem 6-20
If a quadrilateral is an isosceles trapezoid,
______________________________.
then its diagonals are congruent
A
D
B
C
The diagonals of isosceles trapezoid ABCD are:
AC & ____
BD
____
So, ____
AC  _____
BD
Theorem 6-21
If a quadrilateral is a trapezoid then:
1). _____________________________________
the midsegment is parallel to the bases
2). _____________________________________
the length of the midsegment is half
_____________________________________
the sum of the lengths of the bases
A
B
F
E
C
D
1
EF   AB  DC 
2
𝑇𝑈 is the midsegment of trapezoid WXYZ. What is x?
W
Z
6x-12
1
TU   XY  WZ 
2
1
2 x  10    6 x  12   18 
2
2  2 x  10   6 x  6
4 x  20  6 x  6
14  2x
7x
2x+10
U
T
X
18
Y
What is a Kite
If a quadrilateral is a kite, _____________________
then it has two pairs of
____________________________________________
consecutive sides congruent and no opposite
________________.
sides congruent
A
D
B
D
B
A
C
Another
example of a
kite
C
Theorem 6-20
If a quadrilateral is a kite,
__________________________________.
then its diagonals are perpendicular
A
D
B
C
AC & ____
BD
The diagonals of kite ABCD are: ____
So, ____
AC  _____
BD
Properties of Kites
T
In kite STAR, ST=_____
TA
SR=_____
RA
MA
SM=_____
SA  _____
TR
S
M
TSR  
_______
TAR
STM  
_______
ATM
TRS  
_______
TRA
R
A
Homework: p.394 #7-23 odd, 28-36 even
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