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# 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).

Given, in $$\triangle ABC$$, D and E are the mid points of AB and AC respectively, such that,

We have to prove that: DE || BC.

Since, D is the midpoint of AB
=>$$\frac{AD}{BD}$$ = 1……………………………….. (i)

Also given, E is the mid-point of AC.
AE=EC
=> $$\frac{AE}{EC}$$ = 1

From equation (i) and (ii), we get,
$$\frac{AD}{BD} = \frac{AE}{EC}$$

By converse of Basic Proportionality Theorem,
DE || BC

Hence, proved.