Angle Bisector
Overview
An angle bisector splits an angle into two congruent angles, and, just like the perpendicular bisector, it carries a distance property: every point on the bisector is the same distance from the two sides of the angle. The three angle bisectors of a triangle meet inside the triangle at the incenter, which is equidistant from all three sides. Most problems in this lesson come down to one move — the two halves of a bisected angle have equal measures.
Vocabulary
- Angle Bisector
- A segment or ray that divides an angle into two congruent angles.
- Equidistant
- The same distance from two or more points or objects; a point on an angle bisector is equidistant from the sides of the angle.
- Concurrent
- Three or more lines or segments that intersect at a single point.
- Incenter
- The point where the angle bisectors of the three angles of a triangle meet; it is equidistant from the three sides of the triangle and always lies inside the triangle.
Main Ideas
- An angle bisector creates two angles of equal measure, each half the measure of the original angle.
- Any point on the bisector of an angle is equidistant from the sides of the angle.
- A triangle has up to three angle bisectors, and they always intersect inside the triangle at the incenter.
- The incenter is equidistant from the sides of the triangle.
- When an angle and its half are both given as expressions, the whole angle equals twice the half — not the half itself.
Lesson Notes
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Lesson Video
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Practice Problems
Want More Practice?
Download the practice worksheet for this lesson, work the problems, then check your work with the solutions.