Describe a process you would use
to create the perpendicular
bisector to a segment AB using
only an unmarked straightedge
and an unmarked compass.
To create the perpendicular bisector to a segment AB using only an unmarked straightedge and an unmarked compass, follow these steps:
1. Start by marking points A and B on a piece of paper.
2. With the compass, create two arcs on either side of the line segment AB. The arcs should intersect the line segment at two different points. Label these points C and D.
3. Without adjusting the compass, place the compass point on point C and draw an arc above the line segment AB.
4. Repeat the previous step with the compass point on point D, drawing an arc below the line segment AB.
5. Without adjusting the compass, place the compass point on point C and draw an arc that intersects the arc from step 4 (below AB). Label the point of intersection as E.
6. Repeat the previous step with the compass point on point D, drawing an arc that intersects the arc from step 3 (above AB). Label the point of intersection as F.
7. Use the straightedge to draw a line passing through points E and F. This line will be the perpendicular bisector of segment AB.
By following these steps, the perpendicular bisector of segment AB can be constructed using only an unmarked straightedge and an unmarked compass.