How can you construct a perpendicular bisector of a given segment using only two parallel edges of a straightedge with out usign any mesurements on the ruler and compass?

Answer 1

Do I have a compass to use or not ? It's not clear from your question, but since you mentioned it at the end of the question, I'll assume that I do have a compass, and in that case, I only need one straight-edge. 1). Plant the compass on one end of the line segment, open it to more than half the length of the segment, draw a long arc that crosses the segment. 2). Keep the same opening, pick up the compass. 3). Plant the compass on the other end of the segment, draw another long arc that crosses the segment. 4). Sell the compass. 5). The two arcs intersect at two points on opposite sides of the segment. With your straight edge, draw a line between these two points. That line is the perpendicular bisector of the original segment.