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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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Trapezoid A quadrilateral with 1 pair of opposite sides parallel

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**A trapezoid with congruent legs**

Isosceles Trapezoid 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<E=125°**

Find DF _______ m<C _________ m<D _________ m<F _________ D E = 125° F C 10 55 125 55

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**Midsegment of a Trapezoid**

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

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**Example: Find the length of the midsegment MN**

B C M N 12 10 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**

Kites A quadrilateral with 2 pairs of consecutive congruent sides

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**Properties of Kites There are 2 pairs of consecutive sides congruent**

x There are 2 pairs of consecutive sides congruent There is exactly 1 pair of congruent angles Diagonals are perpendicular

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**Example: RSTV is a kite. Find m<R___________ m<S___________**

m<T___________ 70 m<S=125 since <S and <U are congruent 125 x+x = 360 2x+280=360 2x = 80 x=40 40 T R U S 125 x+30 x x=40=m<T x+30 = =70 = m<R

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**Example: GHJK is a kite. Find HP**

Since the Diagonals are perpendicular, HPG is right. You can use the Pythagorean Thm. a2+b2=c2 42+x2=52 16+x2=25 x2=9 x=3 H J K G 5 4 X P

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