To create the perpendicular bisector to a segment AB using only an unmarked straightedge and an unmarked compass, you can follow the following steps:
1. Place the compass's needle at point A and draw an arc that intersects the segment AB at two points. Label these points P and Q.
2. Without changing the compass's width, place the needle at point B and draw another arc that intersects the segment AB at two different points. Label these points R and S.
3. Use the straightedge to draw a straight line passing through points P and Q. This line will extend beyond segment AB.
4. Use the straightedge to draw a straight line passing through points R and S. This line will also extend beyond segment AB.
5. Label the intersection of the two lines as point M.
6. Use the compass to measure the distance between points A and M. Keep the compass's width unchanged.
7. Place the compass's needle at point M and draw an arc that intersects the line passing through points P and Q at two different points. Label these points X and Y.
8. Without changing the compass's width, place the needle at point M and draw another arc that intersects the line passing through points R and S at two different points. Label these points Z and W.
9. Use the straightedge to draw a straight line passing through points X and Y. This line will intersect the line passing through points R and S.
10. Label the intersection point of the two lines as point N. This point is the perpendicular bisector to segment AB.
By following these steps, you can create the perpendicular bisector to segment AB using only an unmarked straightedge and an unmarked compass.
Describe a process you would use to create the perpendicular bisector to a segment AB using only an unmarked straightedge and an unmarked compass.
(3 points)
1 answer
1 answer