Question 85736: What is the locus of points in a plane equidistant from the sides of an angle.
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! The locus of these points is the line that is the bisector of the angle. To convince yourself
of this, draw an angle and then bisect it. Next, pick any point on the angle bisector and
from that point construct perpendiculars to the two sides of the angle. You can see that these
perpendiculars are equal in length. This is not a rigorous proof of that but you can make
it "correct" by noticing that the right angles, the bisected portions of the original
angle, and the common side of the two triangles (the bisector) form a pair of congruent
triangles. Therefore, the length of the perpendiculars to each side of the bisector
are congruent and, therefore, equal in length. Difficult to put into words, but if you play
with it for a while you'll see how this works.
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Hope this helps you to understand the problem.
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