Using Theorem 6.2, 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).

We know that theorem 6.2 tells us if a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side. (Converse of Basic Proportionality Theorem)

In ΔABC,

D is the midpoint of AB

⇒ AD = BD

AD/BD = 1............ (i)

E is the midpoint of AC

AE = CE

⇒ AE/CE = 1........ (ii)

From equations (i) and (ii)

AD/BD = AE/CE = 1

AD/BD = AE/CE

In ΔABC,  according to theorem 6.2 (Converse of Basic Proportionality theorem),

Since, AD/BD = AE/CE

Thus, DE || BC

Hence, proved.