Question

ab ≅ cb
reason:
select 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:

Step1: Analyze the given statement

The statement is \(\overline{AB}\cong\overline{CB}\). We need to check the options for the reason.

Step2: Evaluate each option

• Given: If it is stated in the problem - context that \(\overline{AB}\cong\overline{CB}\), then "Given" is the appropriate reason.
• Reflexive Property: The reflexive property is for a segment being congruent to itself (\(\overline{AB}\cong\overline{AB}\)), so this is not relevant here.
• A segment bisector divides a segment into two congruent segments: This would be relevant if we knew there was a bisector involved in creating the congruent segments, but no such information is given.
• A mid - point divides a segment into two congruent segments: This would be relevant if we knew there was a mid - point involved in creating the congruent segments, but no such information is given.

Answer:

Given