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State and prove the converse of BPT theorem !!!! |
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Answer» nd prove the converse of BPT theorem.✍️Statement :-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 :-∆ABC and a line DE intersecting AB at D and AC at E, such that : ✍️To prove:-We have to prove that DE || BC.✍️Construction:-Draw DE' parallel to BC.✍️Proof:-Since DE' || BC,By theorem 6.1, By theorem 6.1, If a line is drawn parallel to ONE side of a triangle to intersect other two sides not distinct points, the other two sides are divided in the same ratio.And given that, From ( 1 ) and ( 2 ), ADDING 1 on both sides,Thus, E and E' coincide.Since, DE' || BC.Therefore, DE || BC. |
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