Question

Using Basic Proportionality Theorem prove that a line drawn through the mid point of one side of a triangle
parallel to another side bisect the third side-​

Answer 1

Given:

In △ABC,D is midpoint of AB and DE is parallel to BC.

∴ AD=DB

To prove:

AE=EC

Proof:

Since, DE||BC

∴ By Basic Proportionality Theorem,

AD/DB=AE/AC

Since, AD=DB

AE/EC=1

∴AE=EC

Answer 2

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.

To prove, E is the midpoint of AC.

Since, D is the midpoint of AB

So,AD=DB

⇒ AD/DB=1.....................(i)

In triangle ABC,DE||BC,

By using basic proportionality theorem,

Therefore, AD/DB=AE/EC

From equation 1,we can write,

⇒ 1=AE/EC

So,AE=EC

Hence, proved,E is the midpoint of AC.