6-5 Trapezoids and Kites 2/15/17 Objective: To verify and use properties of trapezoids and kites. BASE ANGLES: two angles that share a base of a trapezoid THEOREM 6-15 The two pairs of base angles of an isosceles trapezoid are congruent. W base X W & X are a pair of base angles. Base Angles leg leg Y & Z are another pair of base angles. Y Z base

Ex: ABCD is an isosceles trapezoid and m B = 102 Ex: ABCD is an isosceles trapezoid and m B = 102. Find m A, m C, and m D. C = 102°(base angles =) A = 78°(supp to B) D = 78°(base angles =) B C 102° A D

In the isosceles trapezoid, m S = 70. Find m P, m Q, and m R. Angle P = 110 Angle Q = 110 70° Angle R = 70 R S Theorem 6-16 The diagonals of an isosceles trapezoid are congruent.

THEOREM 6-17 The diagonals of a kite are perpendicular THEOREM 6-17 The diagonals of a kite are perpendicular. Ex: Find m 1, m 2, and m 3 in the kite. Angle 1 = 90 (diagonals of kite are perpendicular) B Angle 2 = 58 (180 – 32 – 90) 32° 3 Angle 3 = 32 (Δ ABD = Δ BCD; CPCTC ) 1 2 A C D

Find m 1, m 2, and m 3 in the kite. Angle 1 = 90 (diagonals of kite are perpendicular) Angle 2 = 46 (Δ’s are congruent; CPCTC ) Angle 3 = 44 (180 – 90 – 46) 46° 1 2 3

ABCD is an isosceles trapezoid If m A = 45, find m B, m C, and m D. If AC = 3x – 16 and BD = 10x – 86, Find x GHIJ is a kite 1) Find m 1 2) Find m 2 3) Find m 3 4) Find m 4 45° 135° 135° x = 10 H 4 50° G I 3 1 2 19° J 90° 19° 71° 40°

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