Question

Using the Theorem, prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side.

Answer 1

Consider the figure in which PQ is a line segment joining the mid-points P and Q of line AB and AC respectively.
i.e., AP = PB and AQ = QC

It can be observed that
$\frac{AP}{PB}=\frac{1}{1}$ and $\frac{AP}{PB}=\frac{1}{1}$

∴$\frac{AP}{PB}=\frac{AQ}{QC}$

Hence, by using the basic proportionality theorem, we obtain
PQ || BC

Hence Proved