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Geometry
Objective :
Lesson Notes 8.6A
Recognize and apply the properties of trapezoids.
trapezoid: a quadrilateral with exactly one pair of parallel sides.
bases: the parallel sides of a trapezoid are called its bases.
legs: the nonparallel sides of a trapezoid are called its legs.
base angles: the pair of angles formed by a base and one of the legs.
bases
base angles
leg
leg
base angles
Note: A trapezoid does not satisfy the definition for a parallelogram.
isosceles trapezoid: a trapezoid with congruent legs.
Theorem 8.18: Both pairs of base angles of an isosceles trapezoid are congruent.
Theorem 8.19: The diagonals of an isosceles trapezoid are congruent.
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Example 3 (p 440): Identify Trapezoids
ABCD is a quadrilateral with vertices A(5, 1), B(−3, −1), C(−2, 3), and D(2, 4).
a.
Verify that ABCD is a trapezoid.
b.
Determine whether ABCD is an isosceles trapezoid.
midsegment (or median) of a trapezoid: the segment that connects the midpoints of the legs
of a trapezoid.
Theorem 8.20: The median of a trapezoid is parallel to the bases and its measure is one-half
the sum of the measures of the bases.
midsegment 
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base1  base2
2
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Example 4 (p 441): Median of a Trapezoid
DEFG is an isosceles trapezoid
with median MN .
E
M
D
2
1
5
6
3
b. Find m1, m2, m3, and m4, if m1 = 3x + 5 and m3 = 6x – 5.
c. What relationship exists between 3 and 5? Between 6 and 4?
A7a p 442-444 #10, 13-19, 22, 32, 34
A7b Lesson 8.6 Skills Practice / Practice
A7c p 442-444 #11, 19, 25, 34
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N
4
a. Find DG if EF = 20 and MN = 30.
 HW
F
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G
Geometry
Lesson Notes 8.6B
Objective : Recognize and apply the properties of kites.
kite: a quadrilateral with exactly two distinct pairs of consecutive sides congruent.
Properties of a kite:
The diagonals of a kite are perpendicular.
The long diagonal bisects a pair of opposite angles.
One set of opposite angles (on the short diagonal) is congruent.
 HW
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A8a fms-Worksheet 8.6 Kites
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