Question

Using the basic proportionality theorem, prove that a line drawn through the mid-points of one side of a triangle parallel to another side bisects the third side.

Answer 1

Consider the given figure in which PQ is a line segment drawn through the mid-point P of line AB, such that PQ || BC

By using the proportionality theorem, we obtain
$\frac{AQ}{QC}=\frac{AP}{PB}$
$\frac{AQ}{QC}=\frac{1}{1}$
$\Rightarrow$AQ = QC
Or, Q is the midpoint of AC