Using Theorem 6.1, prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side. (Recall that you have proved it in Class IX).

We know that theorem 6.1 states that “If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio (Basic Proportionality theorem)”.

In ΔABC, D is the midpoint of AB

Therefore,

AD = BD

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

Now,

DE || BC

⇒ AE/EC = AD/BD [Theorem 6.1]

⇒ AE/EC = 1 [From equation (1)]

⇒ AE = EC

Hence, E is the midpoint of AC.