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State and prove Thales Therom |
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Answer» Answer: Statement: If a line is DRAWN PARALLEL to one side of a triangle, to interest the other two SIDES at INDISTINCT points, the other two sides are divided in the same ratio. Given: - In △ABC,DE∥BC To prove:- AD/DB = AE/EC Construction:- BE and CD are joined. EF⊥AB and DN⊥AL are drawn. Proof:- ar(△ADE) = 1/2×AD×EF =1/2×AE×DN ar(△BDE) = 1/2×BD×EF ar(△CDE) = 1/2×EC×DN ar(△ADE)/ar(△BDE) = 1/2×AD×EF/1/2×BD×EF ........(1) ar(△ADE)/ar(△CDE) = 1/2×AE×DN/1/2×EC×DN ........(2) But, ar(△BDE) = ar(△CDE) ..............(3)
as they are on the same base DE and DE∥BC from (1), (2) and (3) we GET AD/DB = AE/EC |
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