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Transcript 
6.5
 Use
properties of trapezoids.
EQ: How do you Identify a
trapezoid and apply its properties?
trapezoid
A
quadrilateral with exactly one pair
of parallel sides.
 The parallel sides are called the
bases.
 The nonparallel sides are called the
legs.
trapezoid
A
quadrilateral with exactly one pair
of parallel sides.
 The parallel sides are called the
bases.
 The nonparallel sides are called the
legs.
 A trapezoid has two pairs of base
angles.
trapezoid
A
quadrilateral with exactly one pair
of parallel sides.
 The parallel sides are called the
bases.
 The nonparallel sides are called the
legs.
 A trapezoid has two pairs of base
angles.
isosceles trapezoid.
 If
the legs of a trapezoid are
congruent.
Theorem 6.12
 If
a trapezoid is isosceles, then each
pair of base angles is congruent.
Theorem 6.13
 If
a trapezoid has a pair of congruent
base angles, then it is isosceles.
Example 1
Find Angle Measures of Trapezoids
PQRS is an isosceles trapezoid.
Find the missing angle measures.
SOLUTION
1. PQRS is an isosceles trapezoid
So, mR = mS = 50°.
2. Because S and P are same-side interior angles & are
supplementary. So, mP = 180° – 50° = 130°.
3. Because Q and P are a pair of base angles of an
isosceles trapezoid, mQ = mP = 130°.
Checkpoint
Find Angle Measures of Trapezoids
ABCD is an isosceles trapezoid. Find the missing angle
measures.
1.
ANSWER
mA = 80°;
mB = 80°;
mC = 100°
2.
ANSWER
3.
ANSWER
mA =
110°; mB
= 110°;
mD = 70°
mB = 75°;
mC =
105°; mD
= 105°
 The
midsegment of a trapezoid is
the segment that connects the
midpoints of its legs.
Example 2
Midsegment of a Trapezoid
Find the length of the midsegment
DG of trapezoid CEFH.
SOLUTION
Use the formula for the midsegment of a trapezoid.
1
Formula for midsegment of a trapezoid
DG = (EF + CH)
2
1
Substitute 8 for EF and 20 for CH.
= (8 + 20)
2
1
Add.
= (28)
2
= 14
ANSWER
Multiply.
The length of the midsegment DG is 14.
Checkpoint
Midsegment of a Trapezoid
Find the length of the midsegment MN of the trapezoid.
4.
ANSWER
11
ANSWER
8
ANSWER
21
5.
6.
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