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Honors Geometry Section 8.4 The Side-Splitting Theorem We can use similar triangles to find the measures below. Why is AEB ~ ADC? AA We can use similar triangles to find the measures below. Why is AEB ~ ADC? 21 BE 14 35 39 AD 35 BE 819 BE 23.4 21 AD 490 AD 23. 3 35 AC = _____ 9. 3 ED = _____ AD = 23 _____ .3 23.4 BE = _____ 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 One obvious proportion resulting from this theorem would be ET EC TA CH but others that are useful are ET EC EA EH or…….. or EA TA EH CH Example: Consider the figure on the right. 1) TA = 6 AX = 10 TE = 8 TS = ______ 21. 3 8 6 10 6 8 16 TS 2) TA = 5 TX = 14 ES = 12 2 6 TE = __________ 3 5 TE 9 12 5 14 12 3) TA = 8 AX = 12 TS = 30 TE = _____ 12 8 TE 20 30 8 30 12 4) TA = 5 AX = 8 AE = 3 XS = ____ 7.8 5 3 13 XS 5 3 8 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. Examples: Complete each proportion. WX YZ XY WZ YZ xZ