What must you do to construct the midpoint of a segment? a. measure half its length c. construct an angle bisector b. measure twice its length d. construct a perpendicular bisector

To construct a midpoint of the segment, the answer is 
D. construct a perpendicular bisector.
a perpendicular bisector is a straight line that the cuts the segment perpendicularly, at the midpoint of the segment.
a perpendicular bisector can be drawn using the following steps,
place the compass at one endpoint of the segment and draw a circle around it, circle A and place the compass on the other endpoint and draw another circle named circle B.p 
circle A and B coincide at 2 points, join these 2 points and this straight line segment is the perpendicular bisector.

To construct the midpoint of a segment you construct the perpendicular bisector. This bisector will intersect the segment at the midpoint since a bisector divides a segment into two congruent segments.