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Triangle Proportionality Theorem (AKA The Side-Splitting Theorem)

Triangle Proportionality Theorem (AKA The Side-Splitting Theorem). A line parallel to one side of the triangle divides the other two sides proportionally Two-Transversal Proportionality Corollary Three or more parallel lines divide two intersecting transversals proportionally. Example 1.

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Triangle Proportionality Theorem (AKA The Side-Splitting Theorem)

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  1. Triangle Proportionality Theorem(AKA The Side-Splitting Theorem) • A line parallel to one side of the triangle divides the other two sides proportionally Two-Transversal Proportionality Corollary • Three or more parallel lines divide two intersecting transversals proportionally

  2. Example 1

  3. Example 2 Find the remaining lengths.

  4. Triangle Angle Bisector Theorem • An angle bisector of a triangle divides the opposite side into two segments whose lengths are proportional to the lengths of the two other sides. B D A C

  5. Example 1 Find RV and VT.

  6. Example 2 Find AC and DC.

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