ANGLE BISECTOR
Definition Of Angle Bisector
Angle Bisector is a ray that divides an angle into two equal parts.
More about Angle Bisector
Angle bisector is also called the internal angle bisector.
Angle bisectors of a triangle intersect at a point called incenter of the triangle.
A line or a line segment can also be an angle bisector at times. For example, the angle bisectors of polygons are line segments.
Examples of Angle Bisector
In the example shown, OA is the angle bisector. It divides 600 into two equal parts (i.e. two 300's).
Video Examples: Angle Bisector - Geometry Help
Solved Example on Angle Bisector
Ques: In the given figure, 
is the angle bisector of ∠AOB and 
is the angle bisector of ∠COB. If m∠AOC = 3y - 4 and m∠COD = 28, then find the value of y.
Choices:
A. 560
B. 280
C. 200
D. 1120
Correct Answer: C
Solution:
Step 1: m∠COD = 28, so m∠BOC = 56, because is an angle bisector of ∠COB.
Step 2: m∠BOC = 56 implies that m∠AOC = 56, because bisects ∠AOB.
Step 3: So, 3y - 4 = 56 gives y = 200.
Quick Summary
- An angle bisector divides an angle into two congruent angles.
- Angle bisectors of a triangle intersect at the incenter.
- Angle bisectors can be lines, line segments, or rays.
🍎 Teacher Insights
Use hands-on activities with paper folding or compass and straightedge constructions to help students visualize angle bisectors.🎓 Prerequisites
- Angles
- Rays
- Degrees
- Congruence
Check Your Knowledge
Q1: If ray BD bisects angle ABC, and angle ABC measures 80 degrees, what is the measure of angle ABD?
Q2: The angle bisectors of a triangle intersect at a point called the?
Frequently Asked Questions
Q: What is the difference between an angle bisector and a median?
A: An angle bisector divides an angle into two equal angles, while a median connects a vertex to the midpoint of the opposite side.
Q: Can an angle bisector also be an altitude of a triangle?
A: Yes, in an isosceles or equilateral triangle, the angle bisector of the vertex angle is also an altitude and a median.