Question

Using 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. (Recall that you have proved it in Class IX).

Answer 1

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

By using basic proportionality theorem, we obtain

`(AQ)/(QC) = (AP)/(PB)`

`(AQ)/(QC) = 1/1`  (P is the midpoint of AB ∴ AP = PB)

⇒ AQ = QC

Or, Q is the mid-point of AC.