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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.
53º 127º 127º Because it is an isosceles trapezoid, the base angles are congruent. Therefore m <A = m <B, and m <D = m <C 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
19.5 5x + 3
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Find x 45 52.5 10x + 15
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Page 546, #3 – 15,
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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 2√13 6√5
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Find XY, YZ, WZ, and WX 5√5 √461
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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 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 mó G = 360 80º 280 + mó G = 360 mó G = 80
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Find the missing angles
mó F + mó G = 360 240 + mó F + mó G = 360 mó F + mó G = 120 mó F = mó G
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