It is to bisect the angle into two equal angles.
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bisect
An angle bisector.
When you divide an angle into two equal angles you are drawing a line called a bisector.
equal
A bisector is a line that divides an angle into two equal parts. For example: in a right-angle (90 degrees) a bisector will cut the angle into two, each being 45 degrees.
Angle bisector
A midpoint is a point that divides a segment into two congruent segments. A angle bisector is a ray that divides an angle into two congruent angles.
Two equal angles would be the result