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  • 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).

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).

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Solution:

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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