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Published byAdam Sherman Modified over 9 years ago
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Trapezoids & Kites
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Trapezoid Is a quadrilateral with exactly 1 pair of parallel sides
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Trapezoid A B C D leg BASE
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If the legs are congruent then the trapezoid is an isosceles trapezoid.
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Theorem 6.14 If a trapezoid is isosceles, then each pair of base angles is congruent.
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Theorem 6.15 If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid.
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Theorem 6.16 A trapezoid is isosceles if and only if its diagonals are congruent.
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Midsegment The midsegment of a trapezoid is the segment that connects the midpoints of its legs.
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THM 6.17 The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of its bases
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EX 1 Find the length of MN. 13 PQPQ M N S R 10 16
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EX 2 Find the value of x. 19 15 17 x
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A Kite A quadrilateral with two pairs of consecutive congruent sides, but opposite sides are not congruent.
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Theorem 6.18 If a quadrilateral is a kite, then its diagonals are perpendicular.
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Theorem 6.19 If a quadrilateral is a kite, then exactly one pair of opposite angles is congruent.
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Ex 3 Find the measure of the sides. Round to the nearest tenth. LM = 3.6 LO = 3.6 ON= 5 MN = 5 L M N O 2 3 3 4
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Ex 4 Find the m L. 110 40 100 L M N O
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Ex 5 Find the m L. 35 55 135 xx L M N O
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