Ceva's Theorem


Jim Wilson

Given any triangle ABC with a point M in the interior. Segments through M from each vertex to the opposite sides of the triangle are Cevians and Ceva's theorem says that the product of the ratios of the pairs of segments formed on each side of the triangle by the intersection point is equal to 1, where the ratios are taken in same orientation on each side. Further, if the ratio formed by any three Cevians is equal to 1, then the three Cevians are concurrent.

That is:

Who is Giovanni Ceva?

The usual proof of Ceva's Theorem involves consideration of similar triangles in the augmented figure below.

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