2Objectives:Use properties of trapezoids.Use properties of kites.
3Using properties of trapezoids A trapezoid is a quadrilateral with exactly one pair of parallel sides called bases.A trapezoid has two pairs of base angles. Ex. D and CAnd A and B.The nonparallel sides are the legs of the trapezoid.
4Using properties of trapezoids If the legs of a trapezoid are congruent, then the trapezoid is an isosceles trapezoid.
5Isosceles TrapezoidIf a trapezoid is isosceles, then each pair of base angles is congruent.A ≅ B, C ≅ D
6Isosceles TrapezoidIf a trapezoid is isosceles, then adjacent angles (not bases) are supplementary.<A + <D = 180<B + <C = 80
7Ex. 1: Using properties of Isosceles Trapezoids Given, angle X is 50Find <R, < P and <Q,50°
8Isosceles TrapezoidA trapezoid is isosceles if and only if its diagonals are congruent.ABCD is isosceles if and only if AC ≅ BD.
9Midsegment of a trapezoid The midsegment of a trapezoid is the segment that connects the midpoints of its legs.
10Theorem 6.17: Midsegment of a trapezoid The midsegment of a trapezoid is parallel to each base and its length is one half the sums of the lengths of the bases.MN║AD, MN║BCMN = ½ (AD + BC)
11Ex. 3: Finding Midsegment lengths of trapezoids LAYER CAKE A baker is making a cake like the one at the right. The top layer has a diameter of 8 inches and the bottom layer has a diameter of 20 inches. How big should the middle layer be?