Trapezoids and Kites Section 6.5 June 11, 2016

Today you will learn - Properties of Trapezoids Properties of Kites

Vocabulary

Trapezoid A trapezoid is a quadrilateral with exactly one pair of parallel sides. The parallel sides are the bases. The nonparallel sides are the legs. leg base leg

Isosceles Trapezoid A trapezoid with congruent legs.

Midsegment of a Trapezoid The midsegment of a trapezoid is the segment that connect the midpoints of its legs.

Kite A kite is a quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are NOT congruent.

Theorems about Trapezoids Theorem 6.14 If a trapezoid is isosceles, then each pair of base angles is congruent. D A B C Given: ABCD is a trapezoid AD  BC Conclusion:  A   B and  C  D

Theorems about Trapezoids Theorem 6.15 If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid. A B C Given: ABCD is a trapezoid,  A  B Conclusion: AD  BC D

Theorems about Trapezoids Theorem 6.16 A trapezoid is isosceles if and only if its diagonals are congruent. A B C D If AC  DB then ABCD is isosceles and If ABCD is isosceles then AC  DB

Theorems about Trapezoids Theorem 6.17 The Midsegment Theorem for Trapezoids The midsegment of a trapezoid is parallel to each base and its length is the average of the two bases. A B C D M N MN ll AD, MN ll BC MN=

Theorems about Kites Theorem 6.18 If a quadrilateral is a kite, then its diagonals are perpendicular. A C D B BD  AC

Theorems about Kites Theorem 6.19 If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent. A C D B  B  D and  A  C

Example #1 CDEF is an isosceles trapezoid with CE=10 and  E=95 . Find: a.DF b.  C c.  D d.  F C D E F 95 

Example #2 The vertices of WXYZ are W(-1,2), X(3,0), Y(4,-3), and Z(-4,1). Show that WXYZ is an isosceles trapezoid.

Example #3 A potter crafts a trapezoidal relish dish, placing a divider, shown by AB, in the middle of the dish. How long must the divider be to ensure that it divides the legs in half? 10 inches 8 inches

Example #4 The vertices of KLMN are K(-3,5), L(0,7), M(2,7), and N(3,5). Is KLMN a trapezoid? If it is, tell whether it is isosceles and find its midsegment length. K L M N

Example #5 GHJK is a kite. Find HP

Example #6 RSTU is a kite. Find a.  R b.  S c.  T

Example #7 1.Find the length of each side of the kite shown. 2.If  ADC=92  and  ABC=128  find  BAD and  BCD.

Homework