Definition:Bisection/Bisector
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Definition
A bisector is an object which bisects another object.
Angle Bisector
Let $\angle ABC$ be an angle.
The angle bisector of $\angle ABC$ is the straight line which bisects $\angle ABC$.
In the above diagram, $BD$ is the angle bisector of $\angle ABC$.
Thus $\angle ABD \cong \angle DBC$ and $\angle ABD + \angle DBC = \angle ABC$.
Line Bisector
Perpendicular Bisector
Let $AB$ be a line segment.
The perpendicular bisector of $AB$ is the straight line which:
- is perpendicular to $AB$
- passes through the point which bisects $AB$.
Midpoint of Line
Let $L = AB$ be a line segment whose endpoints are $A$ and $B$.
Let $M$ be a point on $L$ such that the line segment $AM$ is equal to the line segment $MB$.
That is, let $M$ be the bisector of $L$.
Then $M$ is the midpoint of $L$.
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): bisector or bisectrix
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): bisect
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): bisect
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): bisector