TRISECTING A Right angle

           An angle Trisector divides an angle into three equal angles. If the angle is 'θ', the three angles made after trisecting will be 'θ/3'.

Problem: To Trisect a Right Angle ABC

1. Let us consider ∠ABC is right angle, B as vortex,

2. Take a compass and draw an arc cutting Horizontal and vertical lines at D and E as shown.

3. With same radious on compass from point E scribe an arc that cuts previously drawn arc at F, and from point D scribe an arc and it will cut the previously drawn arc at point G. 

4. Then join the points BF, BG 

5. These will form the trisector of the given right angle.

Bisecting an Angle

           An angle bisector divides an angle into equal angles. If the angle is 'θ', the two angles made after bisecting will be 'θ/2'. Angle bisectors can be constructed for an acute angle, obtuse angle, or a right angle too. This angle bisector passes through the vortex of an angle, as shown in the figure.

Problem: To bisect a given Angle ABC

1. Let us consider some angle ∠ABC, B as vortex,

2. Take some length in compass and place your compass on the vertex of the angle, here on point B. Draw an arc that crosses both sides of the angle, lines AB and BC. Mark those points as D,E as shown,

3. Place your compass on one of the intersection points (i.e., D) and draw an arc inside the angle. Do not adjust the compass,

4. Place your compass on the other intersection point (i.e., E) and draw an arc that cuts the previously drawn arc as shown,

5. Mark the intersecting point of arc's as F. Finally, draw a line connecting the vortex B and point F. This is the angular bisector of our angle ∠ABC.

6. You can measure both sides of the angle to check they are equal.