Question

PROVE THAT SUM OF TWO SIDES OF A TRIANGLE IS GREATER THAN TWICE THE LENGTH OF MEDIAM DRAWN TO THIRD SIDE

Answer 1

Let AD is the median of ΔABC ,

Then to Prove that:- AB+AC > 2 AD

Construction:- Draw a Δ BEC , in which AD= DE

So that, AE = 2 AD

Hence, ABEC is a ║gm.

BE = AC (opposite angles of ║gm)

Now, Consider ABE as a Δ.

Remember that the sum of any two sides of a Δ is greater than its third side.

AB + BE > AE

Thus,

AB + AC > 2 AD ( Proved)