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Transcript
6-5 TRAPEZOIDS AND KITES (p. 320-325) Let’s review some terminology that is associated with trapezoids. Example: Sketch a trapezoid and identity the following sides and angles. C D A B The bases of a trapezoid are the parallel sides, while the legs are the nonparallel sides. In an isosceles trapezoid, the legs are congruent. A trapezoid has two pairs of base angles, sometimes referred to as the upper base angles and lower base angles. Each pair of base angles includes a base of the trapezoid. Theorem 6-15 The base angles of an isosceles trapezoid are congruent. You will follow a plan in homework problem #26 and prove this theorem. How do the angles that share or include a leg in a trapezoid compare to each other? Which theorem helps you reach this conclusion? Since certain angle pairs in a trapezoid are congruent and other angle pairs are supplementary, there are good algebra problems involving the angles of a trapezoid. Example: XYZW is an isosceles trapezoid. Also, m X 3x 24 and m W 2x - 14. Find m Y, m Z, and m W by setting up and solving an equation. X W Y Z Do 1 on p. 321. Theorem 6-16 The diagonals of an isosceles trapezoid are congruent. Theorem 6-16 is an easy theorem to prove. To prove it, use congruent triangles. Students can do this during their presentations. Example: In isosceles trapezoid RSTU, RT 2x 14 and SU 8x - 42. Find RT by setting up and solving an equation. R S U T The diagonals of a kite are not always congruent. However, these diagonals do have a relationship to each other. Theorem 6-17 The diagonals of a kite are perpendicular. Theorem 6-17 can be proved without using congruent triangles. You can use the theorem that says if a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment. (Short form: Equidistant pt. pt. on bis.). Example: B A C D In kite ABCD, AB AD. Thus, which point is equidistant from B and D? What other two sides of the kite are congruent? Thus, name a second point that is equidistant from B and D. What special line is AC with respect to BD ? Example: K 2 J 3 67 1 D L M In kite JKLM, JK JM and KL LM. By what method(s) is JKD JMD? If m JMD 67, find m 1, m 2, and m 3. Do 3 on p. 322. Homework p. 322-325: 5,7,11,13,17,18,22,24,26,27,30,31,34,45-49,51-53 18. Solve 2x 2(2x - 3) 66. 27. Solve x 6 2x 90. 34. Yes, if two congruent angles are right angles. The other two angles are also supplementary.