Question

Prove that any two sides of a triangle are together greater than twice the median drawn to third side

Answer 1

this is the answer of the question which you are asking

Answer 2

In triangle ABC,extent AB to D in such a way that AD=AC.

In triangle DBC,

angle ADC=angle ACD (Isosceles property)

Therefore, angle BCD>angle BDC

BD>BC (Greater angle opp. greater side)

Also, AB+AD>BC

AB+AC>BC (Since AD=AC)

Hence,

Sum of two sides of a triangle is always greater than the third side.