8.6 Proportions and Similar Triangles Triangle Proportionality Theorem If a line parallel to one side of a triangle intersects the other two sides, then.

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8.6 Proportions and Similar Triangles

Triangle Proportionality Theorem If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally. If TU ll QS, then R T Q S U > >

Given AB ll ED, find EA C D B E A 8 EA = 4(12) 8 EA = 48 EA = 6 > >

Converse of the Triangle Proportionality Theorem

Determining Parallels Given the diagram, determine whether MN || GH. NHL M G

Proportionality Theorem If three parallel lines intersect two transversals, then they divide the transversals proportionally. UW = VX WY XZ UWY V X Z

7 Using Proportionality Theorems

Theorem 8.7 If a ray bisects an angle of a triangle, then it divides the opposite side into segments whose lengths are proportional to the lengths of the other two sides. If CD bisects <ACB, Then AD = CA DB CB A D B C

9 Using Proportionality Theorems

Given CD=14, find DB. C D B 9 15 A 15 DB = 9(14) 15 DB = 126 DB = 8.4

Solve f

Solve s

x

Find the value of JN. L N J M K

Find the value of the variable. 33 q 11 9