8.5

1
8.5 Use Properties of Trapezoids and Kites
2
Trapezoid
Quadrilateral with one pair of opposite sides
parallel

• Consecutive interior angles are supplementary

m?A m?D 180
base
A
B
m?B m?C 180
leg
leg
D
C
base
3
Midsegment of a Trapezoid

• Connects the midpoints of the legs of a
  trapezoid

base base 2
midsegment
base
midsegment
base
4
Isosceles Trapezoid

• Nonparallel sides of the trapezoid are congruent

• The base angles are congruent

• The diagonals are congruent

B
A
C
D
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Quadrilateral that has two pairs of consecutive
congruent sides
Kite

• Exactly one pair of opposite angles are ?

• Its diagonals are perpendicular

6
1. Find the m?B, m?C, m?D.
53
127
127
7
1. Find the m?B, m?C, m?D.
83
97
83
8
2. Find the length of the midsegment.
20 2
7 13 2
base base 2


midsegment

10
9
2. Find the length of the midsegment.
40 2
22 18 2
base base 2


midsegment

20
10
3. Find x.
1
8 4x
2 x
11
3. Find x.
1
7x 28
x 4
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4. Determine whether the quadrilateral is a
trapezoid. If it is, is it an isosceles
trapezoid?
Yes, it is a trapezoid
Alternate interior angles are ?, so one pair of
parallel lines
No
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4. Determine whether the quadrilateral is a
trapezoid. If it is, is it an isosceles
trapezoid?
No,
No parallel lines
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4. Determine whether the quadrilateral is a
trapezoid. If it is, is it an isosceles
trapezoid?
Yes,
Isosceles trapezoid
Base angles are congruent
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5. WEST is a kite. Find the missing angles.
29 x 95 x 360
2x 124 360
x
2x 236
x 118
x
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5. WEST is a kite. Find the missing angles.
107 88 x 88 360
x 283 360
88
x 77
x
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HW Problem
Section Page Assignment Spiral
8.5 546-548 1, 8-11, 13, 15, 19, 20, 25-29 odd 14-20
20
x x 150 90 360
x
x
2x 240 360
2x 120
x 60