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Ratio of the two splitted fragments created by drawing a perpendicular projection from one vertex (i.e., one angle) of a triangle to its opossite side


In triangle ABC, Let D be the foot of the perpendicular drawn from B onto the opposite side AC. Then, is it that the ratio's AB / BC = AD / DC = <ABD/<DBC ?

I presume it is true. But, can one suggest an analytical proof of this theorem ? Or state otherwise the reason (if it is not true).

It would be of much help.


- Thanks and regards

Sankar Basu

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Linkoping University, Sweden




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