Angle Bisector

Angle Bisector is a ray passing through the vertex of the angle and it divides the angle into two congruent angles.

Properties of Angle Bisector:

• Each point belongs to the bisector and is located at the same distance between the two sides of the angle;
• The two angles obtained are congruent and adjacent;

In the following figure, we have the angle and its bisector .

How to draw an Angle Bisector

To draw the angle bisector of the angle using compass, we follow the following steps:

Step1:

We draw two arcs of a circle with center (the vertex of ) and radius so that the first arc intersects with the leg and the second arc intersects with the leg .

Step2:

Draw arcs of two circles with radius :

• The center of the first circle is the intersection of the first arc with the leg we obtained in step 1;
• The center of the second circle is the intersection of the second arc with the leg we obtained in step 1;
  

  

Step3:

We connect by a ray the vertex of the angle with the intersection of the arcs obtained in step 2.

Angles Bisectors of a Triangle

We saw that each angle had an angle bisector. So a triangle that has three angles can have three angle bisectors.

Following the same steps above, we draw the angle bisectors of triangle below:

• The angle bisector of
  

  
• The angle bisector of
  

  
• The angle bisector of
  

  
  The three angle bisectors intersect at a one point, this point being the center of a circle inscribed with triangle .