AD=DC, because BD is a bisector of AC.
BD is in common.
AD and BD are perpendicular, and so are DC and BD, because BD is perpendicular to AC.
AB^2 = AD^2+BD^2 because ABD is right
BC^2 = DC^2+BD^2 because BDC is right
AB=BC because AD=DC
So, AD=DC, AB=BC and BD is common, and the triangles are congruent.
