What Is the Side Splitter Theorem?


Quick Answer

The side splitter theorem states that if a line parallel to one side of a triangle intersects with the other two sides, it divides those two sides proportionally. This theorem can be used to solve many similar triangle math problems.

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Full Answer

A triangle is made up of three lines: AD, AE and DE. If a line that is parallel to line DE cuts through lines AD and AE, it will create a point on line AD labeled B and a point on line AE labeled C. According to the side splitter theorem, AC is proportional to CE as AB is proportional to BD. This also means AC multiplied by BD is the equivalent to CE multiplied by AB.

A corollary of the side splitter theorem states that if three parallel lines intersect with two transversals, then the intercepted segments of the transversals are proportional. A transversal is a line that intersects with at least two other lines.

Another theorem regarding similar triangles is the angle bisector theorem. This theorem states that if triangle ABC has a line AD bisecting the angle BAC, then AB is proportional to BD as AC is proportional to DC. This also means that AB multiplied by DC is equivalent to BD multiplied by AC.

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