question_answer

The line joining the mid-points of two sides of a triangle is

A) bisector of the third side

B) perpendicular to the third side

C) parallel to the third side

D) None of the above

Correct Answer: C

Solution :

Let \[\Delta ABC\]and D and E be mid-points of AB and AC respectively.

\[AD=DB\] and \[AE=EC\]

\[\Rightarrow \,\,\,\,\frac{AD}{DB}=1\] and \[\frac{AE}{EC}=1\]

\[\Rightarrow \,\,\,\,\,\frac{AD}{DB}=\frac{AE}{EC}\]

\[\Rightarrow \,\,\,\,\,DE\,\,|\,\,|\,\,BC\]

[by the converse of basic proportionality theorem]