Given: abc is a triangle. prove: bc + ac > ba in triangle abc, we can draw a perpendicular line segment from vertex c to segment ab. the intersection of ab and the perpendicular is called e. we know that be is the shortest distance from b to and that is the shortest distance from a to ce because of the shortest distance theorem. therefore, bc > be and ac > ae. next, add the inequalities: bc + ac > be + ae. then, be + ae = ba because of the . therefore, ba + ac > ba by substitution.