Question

Prove that the sum of any two sides of a triangle is greater than twice the length of median drawn to the third side

Answer 1

Δ ADB ≅ ΔEDC [ By SAS congruence criterion.]
--> AB=ED[Corresponding parts of congruent triangles ]
In ΔAEC,
The side opposite to the larger (greater) angle is longer
sum of any two sides of a triangle is always greater than the third side

AC+ED> AE
AE=AD+DE
AD=DE
AD+DE=AD+AD=2AD
ED=AB
AC+AB>2AD