Question

in triangle DEF, if DG is the median ,show that DE +EF+FD>2DG

Answer 1

Hey,
In triangle DEG and triangle DGF,
EG=GF(Median divides a line into two equal parts)
DG=DG(common)
angle DGE=angle DGF(right angles)
Therefore,
triangle DGE is congruent to triangle DGF.
Now,
DE=DF(cpct)
EG=GF(cpct).

Now,
DE+EG>DG(any two sides of a triangle is always greater than the third side)
Similarly,
DF+GF>DG.

On adding both the equations,
DE+FD+EG+GF>2GD
DE+FD+EF>2GD.
Hence, proved.

Hope this helps you!!