How to Construct an Angle Bisector: Step-by-Step Guide and Methods

definition of angle bisector

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

An angle bisector is a line, ray, or segment that divides an angle into two equal parts. Specifically, it divides the angle into two smaller angles that have the same measure. The angle bisector starts from the vertex of the angle and cuts through the angle, splitting it into two congruent angles.

In geometric terms, if we have angle ABC, the angle bisector would start from the vertex B and divide the angle into two equal parts, creating two smaller angles of equal measure, angle CBA and angle CBD.

The angle bisector can be constructed using various methods. One common method is to use a compass and a straightedge. To bisect an angle using this method, follow these steps:

1. Place the compass point at the vertex of the angle (point B in our example) and draw a circular arc that intersects both sides of the angle.
2. Without changing the compass width, move the compass point to where the circular arc intersects one side of the angle (line AB in our example). Draw another circular arc inside the angle.
3. Without changing the compass width, move the compass point to where the circular arc intersects the other side of the angle (line BC in our example). Draw a second circular arc that intersects the first circular arc.
4. Using a straightedge, draw a line connecting the vertex of the angle (point B) to the intersection point of the two circular arcs (point D in our example). This line segment BD is the angle bisector.

It is important to note that an angle bisector is not always visible on a diagram or figure since it is a conceptual line, ray, or segment. However, knowing its existence and properties is crucial in various geometric and trigonometric calculations and proofs.

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