Angle bisector in geometry refers to a line that splits an angle into two equal angles. Depending on the inclination between the two arms, an angle may be acute (less than 90-degrees, say 60-degree angle), obtuse (more than 90-degrees) or right angle (exactly 90-degrees).
Constructing angles is an important part of geometry as this knowledge is extended for construction of other geometric figures as well, primarily the triangles. A number of angles can be constructed simply by bisecting some common angles.
Definition: Also known as the bisector of an angle, it is a line that divides an angle into two equal parts. Every angle has an angle bisector. It is also the line of symmetry between the two arms of an angle, the construction of which enables you to construct smaller angles. Say you are required to construct a 30° angle. This can be performed by creating a 60° angle and then bisect it. Similarly, 90-degree, 45-degree, 15-degree and other angles are constructed using this concept.
You require a ruler and a compass to construct angles and their bisectors. Given a known or unknown ∠PQR, the steps to construct its angle bisector are:
The line that was drawn through Q represents the angle bisector of the ∠PQR.
Note: If an angle bisector bisects a line segment at 90°, it is known as perpendicular bisector of that line.