Proportional Lengths Unit 6: Section 7.6

Theorem 7-3 Triangle Proportionality Theorem Divided Proportionally : If points L and M lie on and and , then and are divided proportionally. A L B C M D Theorem 7-3 Triangle Proportionality Theorem If a line parallel to one side of a triangle intersects the other two sides, then it divides those sides proportionally. Then T P Q R S

Use the Triangle Proportionality Theorem to justify any proportion equivalent to For the diagram, some of the proportions that can be justified are: c a j k b d

Example 1: = If CD = 3, DA = 6, and DE = 3.5, then AB = _________ c. If CB = 12, EB = 8, and CD = 6, then DA = __________ Practice 1: True or false? a. b. c. d. e. f. B A 10.5 E D 12 C True True True False False True

Practice 2: Find the value of x. Corollary : If three parallel lines intersect two transversals, then they divide the transversals proportionally. If then Ans: 4 x 8 1 2 R X S Y T Z

Example 2 If a = 2, b = 3, and c = 5, then d = _________ If a = 4, b = 8, c = 5, then c + d = _________ Practice 3 1.True or false? a. b. c. d. 2. Find the value of x. a c 7.5 b d 15 a c T F b d F F 5 x 45/7 7 9

Theorem 7-4 Triangle Angle-Bisector Theorem: If a ray bisects an angle of a triangle, then it divides the opposite side into segments proportional to the other sides. Example 3 F G E D x 10 12 12x -120 = 240 24 12x = 360 x = 30

Practice 4 Find the value of x. If time: Additional Practice p272 #3-11 odd Homework: Practice Worksheet 7.6 8 Ans: x = 12 14 x 21