explain the basic proportionality theorem with explanation and proof.
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If a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion.
PROOF OF BPT
Construction: Draw EF ⟂ AD and DG⟂ AE and join the segments BE and CD. Note that ΔDBE and ΔECD have a common base DE and lie between the same parallels DE and BC. Also, we know that triangles having the same base and lying between the same parallels are equal in area. Hence Proved.
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