Question

Question- Follow the steps below. Once completed answer the questions that follow.

1. Use a straight edge to draw the line segment AB.
2. Place the compass on one end of the line segment.
3. Set the compass length to any length longer than halfway down the line.
4. Without changing the compass width, draw an arc on each side of the line.
5. Again without changing the compass width, place the compass point on the other end of the line. Draw an arc on each side of the line so that the arcs cross the first two.
6. Using a straightedge, draw a line between the points where the arcs intersect.
Where the line crosses segment AB is the midpoint of the line, and the line is perpendicular to the segment AB, so our new line is the perpendicular bisector of AB. Use your protractor and ruler to check your work. Did it work? If you follow these steps, will you ever get a line that is not the perpendicular bisector? Explain.

Answer 1

The procedure above is the procedure for drawing a perpendicular bisector. The intersection of the arcs will always result to the ends of a line that bisects line segment AB which is also perpendicular to line segment AB. The only condition is that the radius of the arc must be greater than half of the length of the line segment or else the arcs will not intersect.