1. 6.6 – Use Proportionality Theorems

2. 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.

3. Converse of the Triangle Proportionality Theorem If a line divides two sides of a triangle proportionally, then it is parallel to the third side If, then

4. If three ______________ lines intersect two _______________, then they divide the transversals _________________. parallel transversals proportionally

5. If a ray bisects an angle of a triangle, then it divides the ______________ side into segments whose lengths are _________________ to the lengths of the other two sides. opposite proportional

6. 1. Find the length of AB. 6x = 60 x = 10

7. 1. Find the length of AB. 24x = 360 x = 15

8. Use the given information to determine whether Explain your reasoning. Yes

9. Use the given information to determine whether Explain your reasoning. No

10. Solve for x. 18(x – 5) = 15(x – 4) x = 10 18x – 90 = 15x – 60 3x – 90 = –60 3x = 30

11. Solve for x. x = 8 4x = 32

12. Solve for x. x = 6 12x = 72

13. Solve for x. x = 10 3x = 30

14. Solve for x. x = 7.5 8x = 60

15. Solve for x. x = 3x = 7 7373