prove: if P is any point inside triangle ABC, then AB + AC > PB + PC

Question

Triangle geometry

Answer 1

Because P is inside the triangle , PB<AB and PC<AC.

So we can write PB=AB-x and PC=AC-y, where x and y are positive values.

Add these two equations: PB+PC=AB+AC-(x+y). Because x+y is a positive quantity, PB+PC<AB+AC.

Therefore AB+AC>PB+PC QED