Honors Geometry Section 8.4 The Side-Splitting Theorem

1. Honors Geometry Section 8.4The Side-Splitting Theorem

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

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

4. AC = _____ED = _____AD = _____BE = _____

5. 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

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

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

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

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

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

11. 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.

12. Examples: Complete each proportion.