#### Question

Using Converse of basic proportionality theorem, 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).

#### Solution

Consider the given 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

`(AP)/(PB) = 1/1`

and `(AQ)/(QC) = 1/1`

`∴ (AP)/(PB) = (AQ)/(QC)`

Hence, by using basic proportionality theorem, we obtain

PQ || BC

Is there an error in this question or solution?

Solution Using Converse of Basic Proportionality Theorem, Prove that the Line Joining the Mid-points of Any Two Sides of a Triangle is Parallel to the Third Side. Concept: Similarity of Triangles.