Question

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

Answer 1

Answer:

It is the Mid Point Theorem

Given:  

In △ABC, D is the 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

Hope it helps.

Please mark this answer as the brainliest.

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.