# Q7   Using Theorem 6.1, prove that a line drawn through the mid-point of one side of a triangle parallel to          another side bisects the third side. (Recall that you  have proved it in Class IX).

Let PQ is a line passing through the midpoint of line AB and parallel to line BC intersecting line AC at point Q.

i.e.$PQ||BC$   and   $AP=PB$.

Using basic proportionality theorem, we have

$\frac{AP}{PB}=\frac{AQ}{QC}..........................1$

Since $AP=PB$

$\frac{AQ}{QC}=\frac{1}{1}$

$\Rightarrow AQ=QC$

$\therefore$ Q is the midpoint of AC.

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