In ABC, D and E are two points on the side AB such that AD = DE =… - Vidyadip

Question

In $\triangle ABC, D$ and $E$ are two points on the side $AB$ such that $AD = DE = EB$. Through $D$ and $E,$ lines are drawn parallel to $BC$ which meet the side $AC$ at points $F$ and $G$ respectively. Through $F$ and $G$, lines are drawn parallel to $AB$ which meet the side $BC$ at points $M$ and $N$ respectively.Prove that $BM = MN = NC.$

✓

Answer

In $\triangle AEG,$
$D$ is the mid$-$point of $AE$ and $DF \| EG \| BC$
Therefore, $F$ is the mid$-$point of $AG.$
$\Rightarrow AF = FG\dots ....(1)$
Again, $DF \| EG \| BC.$
Therefore,$ FG = GC \dots....(2)$
Similarly, since $GN \| FM \| AB,$
therefore $MB = MN = NC.\dots ...($proved$)$

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