Understanding Angle Bisectors: Definition, Types, and Applications in Geometry and Construction

Definition of Angle Bisector

An angle bisector is a line or ray that divides an angle into two equal parts

An angle bisector is a line or ray that divides an angle into two equal parts. It is a line or ray that starts at the vertex of the angle and divides the angle into two congruent (equal) angles.

There are two types of angle bisectors: interior and exterior angle bisectors.

1. Interior Angle Bisector:
An interior angle bisector is a line or ray that starts at the vertex of the angle and divides the angle into two equal parts within the angle. The interior angle bisector forms two adjacent angles that add up to the original angle.
In the figure below, line BD is the interior angle bisector of angle ABC. It divides angle ABC into two congruent angles, angle ABD and angle CBD.

A————————–B
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D

2. Exterior Angle Bisector:
An exterior angle bisector is a line or ray that starts at the vertex of the angle and extends outside the angle, dividing the exterior angle into two congruent angles.
In the figure below, line BE is the exterior angle bisector of angle ABC. It divides the exterior angle into two congruent angles, angle ABE and angle CBE.

A————————–B
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E

Angle bisectors are important in geometry as they help determine perpendicular lines, identify symmetry in shapes, and solve equations involving angles and triangles. They are also useful in constructions, where you can use an angle bisector to accurately divide an angle into two equal parts using a compass and straightedge.

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