Answer: The answer is (a) Congruent segments.
Step-by-step explanation: We are to select the correct construction among the given options that will determine a mid-point.
When we draw two congruent segments in a same straight line and meeting at a point, then the meeting point will be the mid-point of the combined segments.
For example, in the attached figure, AP and PB are two line congruent segments meeting at a point P. Then, P will be the mid-point of AB.
Thus, (a) Congruent segments is the correct option.