Question

When constructing a perpendicular bisector why must the compass opening be greater than 1/2.

Answer 1

It is critical to open a compass with over half the way in order for the arcs formed to meet for perpendicular bisector.

What is perpendicular bisector?

A perpendicular bisector would be a line that cuts a line segment in half and forms a 90-degree angle at the intersection point. In other words, a perpendicular bisector separates a line segment now at midpoint, forming a 90-degree angle.

Now, consider an example;

When you wish to build a perpendicular line on a line segment, like line AB, you do the following;

1. Set the compass on a radius more than half the length of the line AB.
2. Using A as your center, draw an arc above and below line AB.
3. With the same radius and B as our center, draw additional arcs on top or below line AB to join a first arcs on the both side of the line.
4. Join the two arc intersections to cut line AB at M.

A line AB appears to be bisected perpendicularly as a result. The arcs would not have met if the compass is opened less than half way down line AB.

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