Q. 114.3( 23 Votes )

# Prove that, if a

Answer :

Let a ∆ABC in which a line DE parallel to BC intersects AB at D and AC at E.

To prove DE divides the two sides in the same ratio.  Construction join BE, CD and draw EF AB and DG AC. Proof Here,

[ area of triangle = × base × height] Similarly, Now,

Since,

∆BDE and ∆DEC lie between the same parallel DE and BC and on the same base DE.

So, area (∆BDE) = area(∆DEC) …..(iii)

From Equation (i), (ii) and (iii),

AD/DB = AE/EC

Hence proved.

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