Question

What is the locus of points in the plane of and equidistant from the sides of an angle?

Answer 1

The locus of points in the plane of and equidistant from the sides of an angle is the bisector of the angles between the lines.

Explanation:

The locus of points in the plane of and equidistant from the sides of an angle is the bisector of the angles between the lines, as shown below.

In the figure, we have angle formed by lines `AB` and `CD`. They form two pair of vertically opposite angles, supplementary of each other.

`P_1` is the bisector of obtuse angle formed by the two lines. All points on this are equidistant from the two lines `AB` and `CD`.

`P_2` is the bisector of acute angle formed by the two lines. All points on this too are equidistant from the two lines `AB` and `CD`.