Bisector
A bisector divides one segment into two equal parts.
If the bisector is also perpendicular, then it makes 90° with the segment
The problem states BC is the perpendicular bisector of AD. The following statements are true:
AC=DC because BC is the bisector, both parts must be equal
This is always true, thus choice A is not the correct answer
Angle ACB is 90° as explained above because BD is perpendicular to AD
Also, angle DCB is 90° for the same reason
Thus choice C is not the correct answer.
The length of the segment BC is NOT necessarily equal to CD or AC. The last two segments are congruent, but it doesn't extend to BC.
Thus, choice B is correct. The condition is not always true
Finally, the angle ABC must be congruent with angle DBC because both triangles are similar.
Choice D is not correct.
Answer: Choice B