Constructing the midpoint of a segment

Constructing the midpoint of a segment is probably easier than any other straightedge construction.

Step #1:

Use a ruler and a pencil to construct a segment of any length on a piece of paper as you see it below



Then, fix your compass opening to a distance somewhat bigger than 1/2 the length of segment AB.

You should open your compass large enough, but make sure that the distance is not more than the length of AB.

Step #2:

Put the needle of your compass at A and draw an arc




Put the needle of your compass at B and draw an arc




The two arcs should meet as shown below:




Step #3:

Draw a line joining the two points where the two arcs intersect




The point of intersection of the line and the segment shown with a green point is your midpoint