AD is congruent to CD (given)
AB is congruent to CB (given)
DB is contruent to DB (identity)
Therefore, triangle(ADB) is congruent to triangle(DCB) (side-side-side)
and angle(ADB) is congruent to angle(CDB) (corresponding parts of congruent triangles are congruent)
Since angle(ADB) is congruent to angle(CDG), BD bisects angle(ADC).
AD is congruent to CD (given)
angle(ADB) is congruent to angleCDB) (proven above)
Therefore, triangle(ADE) is congruent to triangle(CDE) (side-angle-side)
and angle(AED) is congruent to angle(CED) (corresponding parts of congruent triangles are congruent)
Since angle(AED) and angle(CED) formf a linear pair (a straight line), angle(AED) and angle(CED) are right angles.
Thus, AC and DB are perpendicular.