Question

ab ≅ ad
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:

The symbol $\overline{AB}\cong\overline{AD}$ indicates that line - segment $AB$ is congruent to line - segment $AD$. When this is stated without any other construction or reasoning shown, the most likely reason is that it is given as a condition in the problem. The reflexive property is used when a segment is congruent to itself ($AB\cong AB$), a segment bisector divides a single segment into two congruent sub - segments (e.g., if $M$ is the mid - point of $AC$, then $AM\cong MC$), and a mid - point divides a segment into two congruent segments which is a special case of a segment bisector. Since no such construction is indicated here, the reason is that it is given.

Answer:

Given