The properties that are true for all angle bisectors are:
C. Cut an angle into two angles, each with half the measure of the original angle
D. Splits an angle into two congruent angles
Properties A and B are not universally true for angle bisectors. Angle bisectors do not necessarily form a 90-degree angle with any segment unless specified under certain conditions. Similarly, B refers to segments, which is not applicable in the context of angle bisectors, as angle bisectors specifically relate to angles rather than segments.