Find the midpoint of a line segement without measuring it in inches, centimeters, ect.

Answer 1

I would use a compass, finding the perpendicular bisector, and noting the point it crosses the line. http://www.mathopenref.com/constcircumcenter.html

Answer 2

Use the compass and straightedge construction technique for bisecting a line.

http://www.mathopenref.com/constbisectline.html