6.5 Trapezoids

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6.5Trapezoids

• Feb 29

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A trapezoid is a quadrilateral with exactly one
pair of parallel sides.
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The parallel sides are the bases.

• The nonparallel sides are the legs.

base
leg
leg
base
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A trapezoid has two pairs of base angles
are one pair
are the other pair
ltA and lt B are supplementary, ltC and ltD are
supplementary. Why?
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If the legs of a trapezoid are congruent, then
the trapezoid is an isosceles trapezoid
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If a trapezoid is isosceles, then each pair of
base angles are congruent
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If a trapezoid has a pair of congruent base
angles, then it is isosceles.
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An isosceles trapezoidhas diagonals that are
congruenthowever the point of intersection is
not the midpoint. So, diagonals do not bisect
each other.
E
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The midsegment of a trapezoid is the segment that
connects the midpoints of its legs.
midsegment
The midsegment of a trapezoid is parallel to the
bases.
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The length of the midsegment is half the sum of
the lengths of the bases
A ½ ( 8 20 )
A 14
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Isosceles Trapezoid
Trapezoid
Characteristics
Both pairs of opposite sides parallel
Diagonals are congruent
Both pairs of opposite sides congruent
At least one right angle
Both pairs of opposite angles congruent
Exactly one pair of opposite sides parallel
Diagonals are perpendicular
All sides are congruent
Consecutive angles congruent
Diagonals bisect each other
Diagonals bisect opposite angles
Consecutive angles supplementary
x
x
x
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This is an isosceles trapezoid. Find the missing
angle measures
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Find the length of the midsegment
M ½( 13 21)
M 17
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This is a trapezoid. Find x
8 ½ ( x 10 )
16 x 10
X 6
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Time to relax and do some problems