Question

ad ≅ cd
reason:
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given
reflexive property
a segment bisector divides a
segment into two congruent
segments
a midpoint divides a segment into
two congruent segments

Explanation:

Since the problem is about congruent segments \(\overline{AD}\) and \(\overline{CD}\), and there is no indication of a segment bisector or mid - point being mentioned in the problem statement (other than the fact that we are just given the congruence relation \(\overline{AD}\cong\overline{CD}\)). The most basic reason for a statement in a geometric proof when no other construction (like bisector, mid - point etc.) is mentioned is that it is given.

Answer:

Given