An angle
bisector is a
line or a
ray that divides an
angle into two equal angles.
The method for constructing an angle bisector with an unmarked ruler and a compass is detailed in
proposition 9 of Euclid's Elements: Book I.
For any
triangle, the
angle bisectors of all three angles coincide at the
incenter (see
incenter for proof).
Given any triangle ABC, and an angle bisector PB of angle ABC where P lies on AC, the following about the ratio of lengths is true.
|A-P| |P-C|
------- = -------
|A-B| |B-C|
A P C
*--------------*-------------*
| / /
| / /
| / /
| / /
| / /
| / /
| / /
| / /
| / /
| / /
| / /
| / /
| / /
|//
*
B