So △ACD and △AC'D are congruent, so C'D=CD.

Because AC=AC', AB+AC=AB+AC'=BC'

And C'D=CD, then BD+DC=BD+DC'.

So you see, it becomes a triangle BDC'. Because the sum of two sides is greater than the third side.

So BD+DC' >；; B.C.

That is, BD+DC is greater than AB+AC.