Understanding Angle Bisectors | Definition, Theorem, and Construction | Math Explained

Angle Bisector

An angle bisector is a line or line segment that divides an angle into two equal angles

An angle bisector is a line or line segment that divides an angle into two equal angles. In other words, it cuts the angle in half.

To understand this concept, let’s consider an angle ABC. An angle bisector of angle ABC is a line or line segment that intersects the angle at its vertex (point B in this case) and divides the angle into two equal parts. The two new angles formed are angle ABD and angle DBE.

The angle bisector theorem states that if a line or line segment bisects an angle of a triangle, it divides the opposite side of the angle into segments that are proportional to the other two sides. This theorem is commonly used in geometry proofs to establish relationships between sides and angles of a triangle.

Angle bisectors can be constructed using a compass and ruler. To construct the angle bisector of angle ABC, follow these steps:
1. Place the compass at point B.
2. Adjust the compass width to any suitable length and draw arcs that intersect both rays of angle ABC.
3. Without changing the compass width, place the compass at each of the intersection points on the rays of the angle and draw arcs that intersect each other.
4. The intersection point of the two arcs is the vertex of the angle bisector line or line segment.

Angle bisectors have important applications in various fields, such as architecture, engineering, and problem-solving in mathematics. They help in understanding and analyzing geometric shapes and angles, as well as in solving geometric problems involving triangles and other angles.

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