# Angle Bisector

An angle bisector is a line or ray that divides an angle into two congruent angles.

In the figure, the ray $\stackrel{\to }{KM}$ bisects the angle $\angle JKL$.

The angles $\angle JKM$ and $\angle LKM$ are congruent.

So, $m\angle JKM=m\angle LKM$.

Note that any point on the angle bisector is equidistant from the two sides of the angle. Some textbooks call this Angle Bisector Theorem, but this name is usually used for another theorem about angle bisectors in a triangle.

Example :

In the figure, $\stackrel{\to }{BD}$ is an angle bisector. Find the measure of $\angle ABC$.

Since $\stackrel{\to }{BD}$ is an angle bisector,

$m\angle CBD=m\angle ABD$

Therefore,

$m\angle CBD=65°$

$m\angle ABC=m\angle ABD+m\angle CBD$.
$\begin{array}{l}m\angle ABC=65°+65°\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=130°\end{array}$