Question

prove that a line drawn throught the mid point of one side of triangle parallel to another side bisects the third side(By using the basic praportinality therom)

Answer 1

Step-by-step explanation:

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,

DB

AD

=

EC

AE

Since, AD=DB

∴

EC

AE

=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.