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Date: Sec 8-5 Concept: Trapezoids and Kites Objective: Given properties of trapezoids and kites we will solve problems as measured by a s.g.

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A quadrilateral with 1 pair of opposite sides parallel

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A trapezoid with congruent legs

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Properties of Isosceles Trapezoids Legs of an isosceles trapezoid are congruent Base angles of an isos. trap. are congruent Diagonals of an isos trap. are congruent

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Example: CDEF is an isos. Trap. With CE = 10, and m

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The midsegment of a trapezoid is parallel to each base and it length is 1/2 the sum of the lengths of the bases Midsegment A M BC N D MN=1/2 (BC+AD)

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Example: Find the length of the midsegment MN D A B C M N 1210 MN = 1/2(12+10) = 1/2(22) = 11

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Example: 4 7 x 7 = 1/2(4+x) 14 = 4+x 10 = x

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A quadrilateral with 2 pairs of consecutive congruent sides

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Properties of Kites There are 2 pairs of consecutive sides congruent There is exactly 1 pair of congruent angles Diagonals are perpendicular T R U S x

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Example: RSTV is a kite. Find m

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Example: GHJK is a kite. Find HP H J K G 5 4 X P Since the Diagonals are perpendicular, HPG is right. You can use the Pythagorean Thm. a 2 +b 2 =c 2 4 2 +x 2 =5 2 16+x 2 =25 x 2 =9 x=3

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