Prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side (Using basic proportionality theorem).

To prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side

⇒ Let us assume ABC where DE is parallel to BC and D is the midpoint of AB.

Proof:

In ABC, DE||BC

∴ AD = DB

Since, D is the midpoint of AB

⇒ ……..eq(1)

⇒ now we know that basic proportionality theorem if a line drawn to one side of a triangle intersects the other two sides in distinct points, then it divides the other 2 side in the same ratio.

⇒

⇒ 1 = ………eq(2)

From eq(1) and eq(2)

⇒ EC = AE

⇒ E is the midpoint of AC

Hence proved.