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# Using Theorem 6.2, prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side. (Recall that you have done it in Class IX).

Q8   Using Theorem 6.2, prove that the line joining the mid-points of any two sides of a triangle is parallel
to the third side. (Recall that you have done it in Class IX).

Views

Let P is mid point of line AB and Q is mid point of  line AC .

PQ is line joining mid points P and Q of line AB and AC , respectively.

i.e.$AQ=QC$   and   $AP=PB$.

we have,

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

$\frac{AQ}{QC}=\frac{1}{1}...................................2$

From equation 1 and 2 , we get

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

$\therefore$ By basic proportionality theorem , we have $PQ||BC$

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