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Let E be the midpoint of AC; let D be a arbitrary point on AC. Draw BD; draw EF parallel to BD. Then DF divides the triangle in half. How to prove it?

I know that △AFE is equal in area to △EFC for it is on the same base and in the same parallels (I.38 Euclid), however I don't know how to use this fact.

I also know that equality can be proved if △ABF is shown to be two times the area of △DFE.

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1 Answer

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Medians divide triangles in two halves.

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