Use Properties of Trapezoids and Kites

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Use Properties of Trapezoids and Kites

• Chapter 8.5

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Trapezoids

• Trapezoids are quadrilaterals that have 2
  parallel sides
• The parallel sides are called the bases.
• A trapezoid has 1 pair of base angles.
• The non-parallel sides are called the legs.

base
Leg
Leg
base
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Is it a trapezoid?
Are the bases parallel?
Find the slope of each base.
If the slopes are the same, then it is a
trapezoid.
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Isosceles Trapezoids

• Isosceles triangles have 2 congruent sides with 2
  pairs of congruent angles.
• The diagonals of an isosceles trapezoid are also
  congruent.

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If it is Isosceles find the missing angles.
It is isosceles!
53º
127º
127º
Because it is an isosceles trapezoid, the base
angles are congruent.
Therefore m ltA m ltB, and m ltD m ltC
Angle A and Angle D are supplementary. 180 53
127
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Find the missing angles if it is an Isosceles
Trapezoid.
83º
97º
83º
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Midsegments

• A midsegment is a segment that connects 2
  midpoints.
• The midsegment of a trapezoid connects the
  midpoints of the legs.

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Find the length of the midsegment
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Things always have to be more difficult
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Find x
45
52.5
10x 15
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Page 546, 3 15, 25 - 27
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Kites

• A kite is a quadrilateral with 2 pairs of
  congruent sides, but the opposite sides are not
  congruent.

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Diagonals
If the diagonals of a kite are perpendicular,
then what shape is created by the diagonals?
If we are given these side lengths, can we find
the missing sides XY, WX, YZ , and WZ?
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Find XY, ZY, WX, and WZ
6v5
2v13
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Find XY, YZ, WZ, and WX
5v5
v461
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The figure below is a kite, find the missing
angles
What is the sum of the interior angles of a kite?
360
100 40 mó E mó G 360
140 mó E mó G 360
mó E mó G 220
What do we know about the measures of the angles
E and G?
They are congruent!
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Find the missing angles
What do we know about the measures of the angles
F and H?
They are congruent!
110º
60 110 110 mó G 360
80º
280 mó G 360
mó G 80
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Find the missing angles
150 90 mó F mó G 360
240 mó F mó G 360
mó F mó G 120
mó F mó G