# 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. - Mathematics

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).

#### Solution

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.

Is there an error in this question or solution?

#### APPEARS IN

NCERT Class 10 Maths
Chapter 6 Triangles
Exercise 6.2 | Q 7 | Page 129