Question

In triangle ABC ,D is the midpoint of side AB. line DE || SIDE BC. A-E-C.PROVE THAT POINT E IS THE MIDPOINT OF SIDE AC

Answer 1

we are given that ABC be a triangle and D be he mid point of AB and DE||BC so, AD = DB ...(1)so, in triangle, ABC&ADE ∠BAC=∠DAE ...(common angle)as DE||BC so, ∠ADE=∠ABCand ∠AED=∠ACBso, tri(ADE)∼tri(ABC) SO, AC = AE+EC=2AE= > AE = (AC)/2

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