Question

Describe a process you would use to create the perpendicular bisector to a segment AB using only an unmarked straightedge and an unmarked compass.

explain

Answer 1

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

1. Place the straightedge on top of segment AB, aligning it in such a way that it extends beyond both ends of the segment.

2. With the compass, draw two arcs on either side of the segment AB, crossing the straightedge. Let's label these arcs as C and D.

3. Without changing the compass width, place the compass pointer on C and draw an arc that intersects the previously drawn arc at point E. Similarly, place the compass pointer on D and draw an arc that intersects the previous arc at point F.

4. Using the straightedge, draw a line connecting points E and F. This line should cut segment AB in half.

5. To ensure that the line you just drew is perpendicular to segment AB, use the compass to draw arcs centered at points E and F, crossing the line. Let's label these arcs as G and H.

6. Without changing the width of the compass, place the compass pointer on G and draw an arc that intersects the previously drawn arc at point I. Similarly, place the compass pointer on H and draw an arc that intersects the previous arc at point J.

7. Finally, use the straightedge to draw a line connecting points I and J. This line will be the perpendicular bisector of segment AB.

By following these steps, you can accurately construct the perpendicular bisector of a given segment using only an unmarked straightedge and an unmarked compass.