Question

have
8. Using Theorem 6.2, prove that the line joining the
mid-points of any two sides of a triangle is parallel
to the third side. (Recall that you have done it in
Class IX).​

Answer 1

Given: In △ABC,D and E are midpoints of AB and AC respectively,

i.e., AD=DB and AE=EC

To Prove: DE∥BC

Proof:

Since, AD=DB

∴

DB

AD

=1............(1)

Also,

AE=EC

∴

EC

AE

=1............(2)

From (1) and (2),

DB

AD

=

EC

AE

=1

i.e.,

DB

AD

=

EC

AE

∴ By converse of Basic Proportionality theorem,

DE∥BC

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.