How to construct the axis of an angle
Kapitoly: Angle, Axis of Angle, Angle transfer, The arc measure of an angle, Oriented angle, Converting slope to angle
Every angle has an axis, which is a line that passes through the vertex of the angle and bisects that angle. It follows from this definition alone that the axis of an angle is equidistant from the first and second arms at each of its points. The axis is usually denoted by the lower case letter o.
Description of the axis of an angle
If we have an angle ABC, the angle axis would look like this:
The axis is drawn with a red line. This line bisects the given angle. This means that if we choose a point on the axis, for example F, then the angles ABF and FBC have the same magnitude.
The angle axis has another nice property: we draw two lines CF and AF. These lines make right angles with the arms of the angle, and the angles BCF and BAF are right angles. Then the segments CF and AF have the same length. If we moved the point F somewhere further along the axis, it would still be true that, equally shifted, the segments CF and AF would have the same length.
How to construct the axis of an angle
Constructing the axis of an angle is no problem, just a compass, a ruler and a pen, or at best a pencil (but we all know there's nothing like drawing with a pen). First, draw an arbitrarily large circle with the centre at the vertex of the angle you want to make. This circle will always intersect the arms of the angle at one point, say M and N.
Then take the circle again an arbitrary distance (feel free to do the same, but it must not be a small radius, you will see why below) and make equally sized circles successively centred at M and then centred at N.
Where the circles intersect, there is one point on the axis, we label the point O. The other point on the axis is at the vertex of the angle. Run a straight line through these points and you have an axis.
