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## 6.5 Trapezoids & Kites

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**6.5 Trapezoids & Kites**Advanced Geometry**TRAPEZOID**A trapezoid is a quadrilateral with exactly one pair of parallel sides.**Parts of a Trapezoid**• The parallel sides are the bases • A trapezoid has two pairs of base angles • The nonparallel sides are the legs of the trapezoid**ISOSCELES TRAPEZOID**If the legs of a trapezoid are congruent, then the trapezoid is an isosceles trapezoid.**THEOREM 6.14**If a trapezoid is isosceles, then each pair of base angles is congruent.**THEOREM 6.15**If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid.**THEOREM 6.16**A trapezoid is isosceles if and only if its diagonals are congruent.**Example**CDEF is an isosceles trapezoid with CE = 10 and measure of angle E = 95 degrees. Find DF, measure of angle C, D, and F.**How?**If we were given the graph of a quadrilateral, how would we prove that it is a trapezoid? How would we prove that it is an isosceles trapezoid?**Example**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.**MIDSEGMENT OF A TRAPEZOID**The midsegment of a trapezoid is the segment that connects the midpoints of its legs.**MIDSEGMENT THEOREM FOR TRAPEZOIDS**The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases.**Example**TU is the midsegment of trapezoid QRSP. Find the length of TU.**Example**MN is the midsegment of trapezoid BCDA. Find the value of x.**KITE**A kite is a quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent.**THEOREM 6.18**If a quadrilateral is a kite, then its diagonals are perpendicular.**THEOREM 6.19**If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.