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# Using Basic proportionality theorem, prove that a line drawn through the mid-points of one side of a triangle parallel to another side bisects the third side.(Recall that you have proved it in Class IX).

Answer :

Given, in $$\triangle ABC$$, D is the midpoint of AB such that AD=DB.

A line parallel to BC intersects AC at E as shown in above figure such that DE || BC.

We have to prove that E is the mid point of AC.

Since, D is the mid-point of AB.
AD=DB
=>$$\frac{AD}{DB}$$ = 1 …………………………. (i)

In $$\triangle ABC$$, DE || BC,

By using Basic Proportionality Theorem,

Therefore, $$\frac{AD}{DB} = \frac{AE}{EC}$$

From equation (i), we can write,
=> 1 = $$\frac{AE}{EC}$$
=> AE = EC

Hence, proved, E is the midpoint of AC.