(Converse of Thales' theorem) If a line divides any two sides of a triangle in the same ratio then the line must be parallel to the third side.
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Converse of Basic Proportionality Theorem: If a line divides any two sides of a triangle in the same ratio, then the line must be parallel to the third side. Given : A Δ ABC and a line intersecting AB in D and AC in E, such that AD / DB = AE / EC. ... Then there must be another line that is parallel to BC.
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