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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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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

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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 TS = ______

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

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

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

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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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