Trapezoids and Kites

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Trapezoids and Kites
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Trapezoids

• A trapezoid is a quadrilateral with _______
  _________ of ____________
• ____________. Draw below labeling bases, two
  pairs of base angles, and legs.

one
pair
parallel
sides
base
leg
leg
base
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Isosceles Trapezoids

• When is a trapezoid isosceles?
• When the two legs are congruent
• What else will you know about an isosceles
  trapezoid?
• Each pair of base angles is congruent

A trapezoid is isosceles if and only if its
diagonals are _____________
congruent
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Example 1. Given a quadrilateral with
coordinates O (0, 0), R (0, 3), S (2, 4), and T
(4, 2). Draw on the coordinate plane below then
prove that ORST is a trapezoid.
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Example 2 Determine the missing angle measures
for each trapezoid below.
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Midsegment Theorem

• The ________________ of a trapezoid is
  ____________ to each base and its length is
  _________ the _________ of the lengths of the two
  bases.

midsegment
parallel
half
sum
Formula
MN 1/2(AB CD)
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Example 3 Determine the length of each midsegment
below.
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Example 4 Find the value of x.
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Kites

• A kite is a quadrilateral that has __ _______ of
  consecutive ______________ sides, but
  _____________ sides are NOT _____________.

pairs
2
congruent
opposite
congruent
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Theorems

• If a quadrilateral is a kite, then its diagonals
  are _________________.

perpendicular
If a quadrilateral is a kite, then exactly ___
_________ of __________ angles are ___________.
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pair
opposite
congruent
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Example 5 EFGH is a kite. Find mltG.
Example 6 Find the side lengths of the kite.
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Property Parallelogram Rectangle Rhombus Square Kite Trapezoid
All sides are congruent. Always Always
Both pairs of opposite sides are congruent. Always Always Always Always
Exactly one pair of opposite sides are parallel. Always
All angles are congruent. Always Always
Exactly one pair of opposite angles are congruent. Always
Diagonals are perpendicular. Always Always Always
Diagonals are congruent. Always Always
Both pairs of opposite sides are parallel. Always Always Always Always
Diagonals bisect each other. Always Always Always Always