2. 8.6 Proportions and Similar Triangles

3. 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 > >

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

5. Converse of the Triangle Proportionality Theorem

6. Determining Parallels Given the diagram, determine whether MN || GH. NHL M G 16 48 21 56

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

8. 7 Using Proportionality Theorems

9. 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

10. 9 Using Proportionality Theorems

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

12. Solve 20 10 8 f

13. Solve. 9 8 10 s

14. 20 12 22 x

15. Find the value of JN. L N J M K 16 3 18

16. Find the value of the variable. 33 q 11 9