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**Honors Geometry Section 8.4 The Side-Splitting Theorem**

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

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**AC = _____ ED = _____ AD = _____ BE = _____**

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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

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

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**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 = ______

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

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3) TA = AX = TS = TE = _____

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4) TA = AX = AE = XS = ____

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**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.

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**Examples: Complete each proportion.**

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