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).

Answer 1

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