Trapezoids and Kites

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Lesson

• Trapezoids and Kites

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Do Now
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Trapezoids
They have only one pair of opposite sides that
are parallel
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If the legs are congruent then the trapezoid is
ISOSCELES
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If a trapezoid is isosceles then each pair of
base angles is congruent
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ISOSCELES
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Example 1 Find the other angles in this
isosceles trapezoid.
D
C
A
B
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If a trapezoid is isosceles then its diagonals
are congruent
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The MEDIAN connects the midpoints of the legs
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Median Theorem for Trapezoids
parallel to each base and its length is half
the sum of the lengths of the bases
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Which means
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Example 2 Find the length of the median MN in
trapezoid ABCD if AB 20 and CD 16.
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EXAMPLE 3
EF is the median of trapezoid ABCD. Find EF.
22 in.
A
B
EF 16
E
F
C
D
10 in.
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EXAMPLE 4
BC is the median of trapezoid MATH. Find MA.
MA 8
A
M
15 in.
C
B
T
H
22 in.
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EXAMPLE 5
BC is the median of trapezoid TRAP. Find TR.
TR 27
T
R
19 in.
C
B
P
A
11 in.
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Kite theorems

• Kite Diagonals Conjecture
• If a quadrilateral is a kite, then its diagonals
  are perpendicular.
• AC BD
• Kite Diagonal Bisector Conjecture
• The diagonal connecting the vertex angles of a
  kite is the _______________________ of the other
  diagonal