Question

describe a process you would use to create the perpendicular bisector to a segment a b using only an unmarked straight edge and an unmarked compass

Answer 1

To create a perpendicular bisector to a segment AB using only an unmarked straightedge and compass, you can follow the following steps:

1. Place the compass needle at point A and draw an arc that intersects the segment AB on both sides. Make sure to keep the compass open to a reasonable distance that can create two visible intersections, but not too wide.

2. Without adjusting the compass size, place the compass needle at point B and draw another arc that intersects the segment AB on both sides. The arcs should intersect with the previous arcs you drew in step 1.

3. Using the straight edge, draw lines connecting the points where the arcs intersected on both sides of the segment AB. Let's call those points C and D respectively.

4. Finally, use the straightedge to draw a line passing through points C and D. This line will be the perpendicular bisector of the segment AB, dividing it into two equal halves.

It is important to note that the accuracy of this method strongly relies on maintaining the same compass size throughout the process and ensuring the arcs intersect the segment AB on both sides.