Find the midpoint of a line segement without measuring it in inches, centimeters, ect.
I would use a compass, finding the perpendicular bisector, and noting the point it crosses the line. http://www.mathopenref.com/constcircumcenter.html
Use the compass and straightedge construction technique for bisecting a line.
http://www.mathopenref.com/constbisectline.html
To find the midpoint of a line segment without measuring it in inches, centimeters, or any other unit, you can use the geometric construction method known as "bisection." Here's how you can do it:
1. Draw a straight line segment using a ruler or any other straight edge. Let's call the endpoints of the line segment A and B.
2. Use your compass to draw two arcs with the same radius, centered at points A and B. Make sure the arcs intersect the line segment at two distinct points on each side.
3. Without adjusting the compass, draw two more arcs with the same radius from the points where the first two arcs intersected the line segment. Again, make sure the new arcs intersect the line segment at two distinct points on each side.
4. Now, using your ruler or straight edge, connect the intersection points of the two arcs on each side of the line segment. This line will pass through the midpoint.
5. The point where the line intersects the line segment is the midpoint of the original line segment.
By following this construction, you can find the midpoint of a line segment without relying on any measurement unit.