Construct an angle of 90° and draw its bisector.

Steps of Construction:

1. Draw line segment AB.

2. With A as centre and any suitable radius draw an arc, cutting AB at C.

3. With C as centre and the same radius, cut the previously drawn arc at D.

4. With D as centre and the same radius, cut the arc at E.

5. With D as centre and the radius more than half DE, draw an arc.

6. With E as centre and the same radius draw another arc which cuts previous arc at F.

7. Join F. So, ∠BAF = 90°

8. Now with C as centre and radius more than half of DC draw an arc.

9. With D as centre and same radius draw an arc which cuts the previous at G.

10. Join AG. Therefore, it is the bisector of ∠ BAF, i.e., 45°