Answer:
By the definition of midpoints, AX and CX are congruent. By the definition of segment bisectors, X is the midpoint of BD, and therefore BX and DX are congruent. Since angle AXD and CXB are vertical angles, they are congruent by the vertical angles theorem. By SAS, triangles AXD and CXB are congruent. By CPCTC, angles A and C are congruent. By converse of alternate interior angles theorem, AD is parallel to CB.
