Without knowing what the dropdown list shows for reasons, it's hard to pinpoint exactly what is expected here.
Angle ACD is congruent to angle BCD because they are corresponding angles between the congruent triangles ∆ACD and ∆BCD.
The triangle congruency is due to angle-angle-side (AAS) similarity:
• angles A and B are congruent - this is given
• angles CDB and CDA are congruent right angles - this is implied by the given detail that CD and AB are perpendicular
• the leg CD is common to both triangles, and CD is of course congruent to itself (reflexive property)
So angles ACD and BCD are congruent, which means they have the same measure, so by definition of angle bisector, CD bisects angle ACB.
QED