Question

1. visit kimeosuccessmatertals.com, read integrated mathematics 1 lesson 8.5, then read the section below.

teacher voice - an angle bisector is a ray that divides an angle into two angles that are congruent. in the figure to the left, $overrightarrow{bd}$ bisects $angle abc$, so that $mangle abd$ is equal to $mangle cbd$. you can use geometric tools to find the angle bisector.
construction - bisecting an angle
construct the angle bisector of $angle m$.

1. place the point of your compass on point $m$, and draw an arc that intersects both sides of the angle. label the points of intersection $p$ and $q$.
2. with $p$ and $q$ as centers, mark off two arcs with equal radii to intersect at a point in the interior of angle $m$. label the intersection of the arcs $r$.
3. now draw $overrightarrow{mr}$, the desired angle bisector.

try this - bisecting an angle

1. construction - use a compass and straightedge to construct the angle bisector of $angle l$.

Explanation:

Step1: Mark arcs on angle sides

Place compass on $L$, draw arc intersecting both sides of $\angle L$. Label intersections $P$ and $Q$.

Step2: Draw intersecting interior arcs

With $P$ and $Q$ as centers (equal radii), draw arcs intersecting inside $\angle L$. Label intersection $R$.

Step3: Draw the angle bisector

Draw ray $\overrightarrow{LR}$; this is the bisector of $\angle L$.

Answer:

The angle bisector is constructed as ray $\overrightarrow{LR}$, which divides $\angle L$ into two congruent angles.