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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).

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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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