Q. 64.2( 43 Votes )

Prove that a line joining the midpoints of any two sides of a triangle is parallel to the third side. (Using converse of basic proportionality theorem)

Answer :

To prove that a line joining the midpoints of any two sides of a triangle is parallel to the third side.


now we know the converse of a basic proportionality theorem is if a line divides any two sides of a triangle in the same ratio then the line must be parallel to the third side.


Let us assume ABC in which D and E are the mid points of AB and Ac respectively such that


AD = BD and AE = EC.



To prove that DE || BC


D is the midpoint of AB


AD = DB


………eq(1)


Also, E is the midpoint of AC


AE = EC


……..eq(2)


From equation (1) and (2) we get



DE || BC by converse of proportionality thereom


Hence, the line joining the mid points of any two sides of a triangle is parallel to three sides.


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