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6.5 Trapezoids & Kites Trapezoid • Is a quadrilateral with exactly 1 pair of parallel sides Trapezoid A BASE C B D BASE If the legs 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. Midsegment •The midsegment of a trapezoid is the segment that connects the midpoints of its legs. THM 6.17 • The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of its bases 1 midsegment base1 base 2 2 EX 1 Find the length of MN. P M 13 S 10 Q 16 N R EX 2 Find the value of x. 19 15 17 x A Kite • A quadrilateral with 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 is congruent. Ex 3 Find the measure of the sides. Round to the nearest tenth. L LM = 3.6 LO = 3.6 ON= 5 MN = 5 2 O 3 3 4 N M Ex 4 Find the mL. L 110 M 100 40 O N Ex 5 Find the mL. L 35 M x O 55 135 N Add Trapezoid and Kite to your foldable. Goal: Identify midsegments and use properties of midsegments of a triangle Midsegment – a segment that connects the midpoints of two sides of a triangle. Midsegment Theorem The segment connecting the midpoints of two sides of a triangle is parallel to the third side and half as long. X B Y AC || XY XY = ½ AC A C Ex 1: UW and VW are midsegments of RST. Find UW and RT. R U UW = 6 RT = 16 V 12 8 T W S Ex 2: X, Y, and Z are the midpoints of UVW. Complete each statement. a. If VW = 6a, then XY = ___ U c. XZ _______. X V b. mWZY = 2b + 1, then mWVU = ______. Y Z d. If YZ = c, then UV = ____ W