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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).

Answer :

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

AD=BD and AE=EC.

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.
=> \(\frac{AE}{EC}\) = 1

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

By converse of Basic Proportionality Theorem,
DE || BC

Hence, proved.

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