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Honors Geometry Section 8.4 The Side-Splitting Theorem.

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Presentation on theme: "Honors Geometry Section 8.4 The Side-Splitting Theorem."— Presentation transcript:

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 some 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 TS = ______

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

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

9 4) TA = 5 AX = 8 AE = 3 XS = ____

10 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.


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