8.5 Trapezoids. You will learn to identify and use the properties of trapezoids and isosceles...
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Transcript of 8.5 Trapezoids. You will learn to identify and use the properties of trapezoids and isosceles...
8.5 Trapezoids
Trapezoids
You will learn to identify and use the properties of trapezoidsand isosceles trapezoids.
1) Trapezoid
Trapezoids
A trapezoid is a ____________ with exactly one pair of ____________.quadrilateral parallel sides
T
P A
R
The parallel sides are called ______.bases
base
baseThe non parallel sides are called _____.legs
leg leg
Each trapezoid has two pair ofbase angles.
base anglesT and R are one pairof base angles.
P and A are the other pair of base angles.
Trapezoids
Theorem8-13
The median of a trapezoid is parallel to the _____, basesand the length of the median equals _______________ of the lengths of the bases.
one-half the sum
C
N
B
D
M
A
MNDCMNAB || ,||
DCABMN 2
1
Trapezoids
C
N
D
M
BA
Find the length of median MN in trapezoid ABCD if AB = 16 and DC = 20
16
20
DCABMN 2
1
20162
1MN
362
1MN
18MN
18
Trapezoids
If the legs of a trapezoid are congruent, the trapezoid is an _________________.isosceles trapezoid
In lesson 6 – 4, you learned that the base angles of an isosceles triangle arecongruent.
There is a similar property of isosceles trapezoids.
Trapezoids
Theorem8-14
Each pair of __________ in an isosceles trapezoid is congruent.base angles
Z Y
XW
XW
YZ
Trapezoids
T
P A
R
60°
Find the missing angle measures in isosceles trapezoid TRAP.
P A
mP = mA
60 = mA
60°
Theorem 8 – 14
T R
P + A + 2(T) = 360
Theorem 8 – 14
60 + 60 + 2(T) = 360
120 + 2(T) = 360
2(T) = 240
T = 120
120°
R = 120
120°
Trapezoids