Question

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

Step-by-step explanation:

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

∴DBAD=1............(1)

Also,

AE=EC

∴ECAE=1............(2)

From (1) and (2),

DBAD = ECAE =1

i.e.,DBAD = ECAE

∴ By converse of Basic Proportionality theorem,

DE∥BC