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)
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.
To create the perpendicular bisector of a segment AB using only an unmarked straightedge and an unmarked compass, follow these steps:
1. Step 1: Place the compass at point A, open it wide enough to reach beyond point B, and draw two arcs intersecting the line segment AB on both sides.
2. Step 2: Without changing the compass radius, place the compass at point B and draw two more arcs intersecting the line segment AB on both sides.
3. Step 3: Draw a straight line connecting the intersection points of the four arcs. This line will be the perpendicular bisector of the segment AB.
Remember to use the straightedge only for drawing straight lines and the compass only for drawing arcs. Do not use any markings or measurements on the straightedge or compass.
To create a perpendicular bisector to a segment AB using only an unmarked straightedge and an unmarked compass, we can follow the process below:
1. Place the compass needle at point A and set the compass length greater than half the length of segment AB.
2. Using the compass, draw an arc on both sides of segment AB.
3. Without adjusting the compass, place the needle at point B and draw another set of arcs that intersect the previous arcs.
4. You should now have four points where the arcs intersect. Label these points as C, D, E, and F, with C and D on one side and E and F on the other side of segment AB.
5. Use the straightedge to connect points C and D as well as points E and F.
6. The line that passes through points C and D should intersect the line that passes through points E and F at a point G.
7. Label the intersection point G.
8. The line passing through point G and perpendicular to segment AB is the perpendicular bisector.
By following these steps, you can construct the perpendicular bisector to segment AB using an unmarked straightedge and an unmarked compass.