Angle Bisector - Definition, Construction, Properties, Examples

An angle bisector can be defined as a ray, line segment or line that divides an angle into two equal parts. In other words, a ray, line segment or line that cuts an angle in two congruent parts is termed an angle bisector.

Properties Of Angle Bisector

• An angle is divided into two equal pieces by an angle bisector.

• Any point on an angle's bisector is equally distanced from the angle's sides or arms.

• It divides the opposite side of a triangle in proportion to the other two sides

Some Important terms

• Angle: An angel is a structure created by two rays that share an endpoint and are referred to as the angle’s sides and vertices, respectively. Angles created by two rays are in the plane where rays are located. The meeting point of two planes also creates angles.

• Bisector: A bisector in geometry can be termed as a ray, line or line segment that divides a figure into two equal parts. It can divide angles as well as line segments.

• Bisect: Bisect in geometry is used for dividing into two exactly equal parts.

Construction Of An Angle Bisector

Step 1: Drawing an angle, \angle ACB .

Step 2: Draw an arc with C as the centre and any suitable radius to intersect the rays AC and CB, say at D and E, respectively.

Step 3: Draw two arcs that will intersect at F by using D and E as the centres and the same radius as in the previous step.

Step 4: Drawing a ray by connecting C and F. The required angle bisector of angle ACB is this ray CF.

An Angle Bisector Of A Triangle

The straight line that divides an angle in a triangle into two equal or congruent angles is known as the angle bisector of a triangle. As a triangle has three vertices, there can be three angle bisectors in it. The incenter of a triangle is the location where these three angle bisectors intersect. All of a triangle's vertices are equally distanced from the incenter. The figure below shows the triangle's angle bisector. The angle bisectors of ABC, BCA and CAB in this case are BD, CE and AF, respectively. G is the incenter, or point of intersection of all three bisectors, and it is located at an equal distance from each vertex.