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.

Trapezoid A quadrilateral with 1 pair of opposite sides parallel

A trapezoid with congruent legs Isosceles Trapezoid A trapezoid with congruent legs

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

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

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)

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

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

A quadrilateral with 2 pairs of consecutive congruent sides Kites A quadrilateral with 2 pairs of consecutive congruent sides

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

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+30+125+125 = 360 2x+280=360 2x = 80 x=40 40 T R U S 125 x+30 x x=40=m<T x+30 = 40+30 =70 = m<R

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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