1. Honors Geometry Section 8.6 Triangle Proportionality Theorem

2. We can use similar triangles to find the measures below. Why is ?

4. AC = _____ ED = _____ AD = _____ BE = _____

5. some The Triangle Proportionality Theorem gives us another way of find some of the lengths from the previous problem. Triangle Proportionality Theorem A line parallel to one side of a triangle will DIVIDE THE OTHER TWO SIDES PROPORTIONALLY

6. One obvious proportion resulting from this theorem would be but others that are useful are or or……..

7. Example: Consider the figure on the right. 1) TA = 6 AX = 10 TE = 8 TS = ______

8. 2) TA = 5 TX = 14 ES = 12 TE = __________

9. 3) TA = 8 AX = 12 TS = 30 TE = _____

10. 4) TA = 5 AX = 8 AE = 3 XS = ____

11. The following theorem could easily be a corollary of the Triangle Proportionality Theorem. Theorem 8.6 Three or more parallel lines will divide two transversals proportionally.

12. Examples: Complete each proportion.