证明：在DC上取一点E ,使BD=ED ,连结AE .
易证三角形ABD 全等于三角形ADE ,所以BD =ED ,AB = AE,角B =角AED .因为角AED =角C +角CAE ,所以角CAE =角C=二分之一角B ,所以AE =EC=AB .所以AB+BD=ED+CE=CD.