Side splitter theorem

A side splitter theorem is a theorem used in geometry to describe a relationship inside a triangle. It applies when a line intersects two sides of a triangle an

A side splitter theorem is a theorem used in geometry to describe a relationship inside a triangle. It applies when a line intersects two sides of a triangle and is parallel to the third side of the triangle.[1] When this happens, the line divides the two sides that it intersects proportionally. It is based on the idea of proportional segments. Instead of creating equal lengths, the theorem creates equal ratios.[2] This means that the parts of one side of the triangle have the same ratio as the corresponding parts of the other side. It can be stated as follows: if a line intersects two sides of a triangle and is parallel to the third side, then it divides those two sides proportionally. This relationship is used to compare segment lengths and show that certain ratios are equal.[3]

References

  1. ↑ https://mckellarmath.com/wp-content/uploads/2025/10/Side_Splitter.pdf
  2. ↑ https://homepages.math.uic.edu/~jbaldwin/CTTIgeometry/geosli3.pdf
  3. ↑ https://www.math.uakron.edu/amc/Geometry/HSGeometryLessons/SideSplitterTheorem.pdf

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