1. Honors Geometry Section 8.4 The Side-Splitting Theorem

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

3. AC = _____ ED = _____ AD = _____ BE = _____

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

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

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

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

8. 3) TA = AX = TS = TE = _____

9. 4) TA = AX = AE = XS = ____

10. The following statement is a corollary of the Side-Splitting Theorem
The following statement is a corollary of the Side-Splitting Theorem. Two-Transversal Proportionality Corollary
Three or more parallel lines will divide two transversals proportionally.

11. Examples: Complete each proportion.