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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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9.3.3.7 Use properties of polygons—including quadrilaterals and regular polygons—to define them, classify them, solve problems and logically justify results.

9.3.3.7 Use properties of polygons—including quadrilaterals and regular polygons—to define them, classify them, solve problems and logically justify results.

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