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.

What do you mean by this? in a proof normally there is two sides. the left side is where you “solve” the problems and write the steps which would be the statement. on the right side, you state your reasons which would be what you did to each step.