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6-6 Properties of Kites and Trapezoids Kite—a quadrilateral with exactly two pairs of congruent consecutive sides. Properties of Kites Theorems 1. If a quadrilateral is a kite, then its diagonals are perpendicular. In a kite, one diagonal is the perpendicular bisector of the other diagonal. Segment AC is the perpendicular bisector of BD 2. If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent. Trapezoid—a quadrilateral with exactly one pair of parallel sides. Each of the parallel sides is called a base. The non-parallel sides are the legs. Base angles of a trapezoid—two consecutive angles whose common side is a base. http://www.mrlarkins.com/geometry/InteractiveTextbook/Ch06/06-05/PH_Geom_ch06-05_Obj1.html Isosceles trapezoid—A trapezoid with congruent legs. http://www.google.com/imgres?q=base+angles+of+a+trapezoid&hl=en&biw=1366&bih=622& Isosceles Trapezoids Theorems 1. If a quadrilateral is an isosceles trapezoid, then each pair of base angles are congruent. http://www.google.com/imgres?q=base+angles+of+a+trapezoid&hl=en&biw=1366&bih=622&tbm=isch&tbnid=QOSXsg7oeD2ggM:&imgrefurl= 2. If a trapezoid has one pair of congruent base angles, then the trapezoid is isosceles. < A is congruent to < B, therefore ABDC is an isosceles trapezoid. 3. A trapezoid is isosceles if and only if its diagonals are congruent. Segment BC is congruent to segment AD, therefore trapezoid ABDC is an isosceles trapezoid. Trapezoid Midsegment theorem—The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases. http://www.google.com/imgres?q=trapezoid+midsegment+theorem&num=10&hl=en&biw=1366 http://www.google.com/imgres?q=trapezoid+midsegment+theorem&num=10&hl=en&biw=