The document provides steps for drawing a fan by bisecting angles. It involves initially dividing a 90 degree angle in half, then bisecting those 45 degree angles to create four equal angles. Arcs are drawn using a compass to locate bisectors and intersection points, dividing the angles further. Finally, a semicircle is drawn to complete the fan shape, using the original diameter as the radius.

1. DRAWING WITH THE BISECTOR
OF AN ANGLE

2. We are going to draw a fan.
Initially, we have the diameter AB of the semicircumference that is going to close the fan.
So, we have a straight angle divided into two halves: two angles of 90o
A B

3. A B
O
STEPS:
1.The first step is to divide each angle of 90o
into two halves. So we have to draw the
bisector of the two angles of 90o . To do this,
center at O and draw an arc with the length
you want. You get the points 1, 2 and 3

4. A B
1
2
O
STEPS:
1.The first step is to divide each angle of 90o
into two halves. So we have to draw the
bisector of the two angles of 90o . To do this,
center at O and draw an arc with the length
you want. You get the points 1, 2 and 3

5. 1
A B
2
3
O
STEPS:
1.The first step is to divide each angle of 90o
into two halves. So we have to draw the
bisector of the two angles of 90o . To do this,
center at O and draw an arc with the length
you want. You get the points 1, 2 and 3

6. 1
STEPS:
2.Now, to draw the bisector of the right angle
formed by 2-O-1, center the compass at 1
and draw an arc further than the middle of
the arc (you can keep the length you had
before, when you drew the first arc) and do
the same centering at 2
A B
2
3
O

7. 1
A B
2
3
O
STEPS:
2.Now, to draw the bisector of the right angle
formed by 2-O-1, center the compass at 1
and draw an arc further than the middle of
the arc (you can keep the length you had
before, when you drew the first arc) and do
the same centering at 2

8. 1
A B
2
3
O
STEPS:
3.Do the same centering at 2 and 3 to draw
the bisector of the other right angle (the one
formed by 2-O-3)

9. 1
A B
2
3
O
STEPS:
3.Do the same centering at 2 and 3 to draw
the bisector of the other right angle (the one
formed by 2-O-3)

10. 1
A B
2
3
O
STEPS:
4.Draw the bisector of both angles. We get the
points 4 and 5

11. 1
A B
2
3
O
4
5
STEPS:
4.Draw the bisector of both angles. We get the
points 4 and 5

12. 1
A B
2
3
O
STEPS:
5.We have the two rights angle divided into two halves. So, we have 4 angles of
45o. Now, we have to divide the four angles of 45o into two halves. We have to
draw the bisector of each angle of 45o. Then, center the compass with the same
length at 1 and 4 and draw two arcs that cross each other
4
5

13. 1
A B
2
3
O
4
5
STEPS:
5.We have the two rights angle divided into two halves. So, we have 4 angles of
45o. Now, we have to divide the four angles of 45o into two halves. We have to
draw the bisector of each angle of 45o. Then, center the compass with the same
length at 1 and 4 and draw two arcs that cross each other

14. 1
A B
2
3
O
4
5
STEPS:
5.We have the two rights angle divided into two halves. So, we have 4 angles of
45o. Now, we have to divide the four angles of 45o into two halves. We have to
draw the bisector of each angle of 45o. Then, center the compass with the same
length at 1 and 4 and draw two arcs that cross each other

15. 1
A B
2
3
O
STEPS:
6.Do the same with the angle 2-O-4
4
5

16. 1
A B
2
3
O
4
5
STEPS:
6.Do the same with the angle 2-O-4

17. 1
A B
2
3
O
STEPS:
7.Do the same with the angle 5-O-2
4
5

18. 1
A B
2
3
O
4
5
STEPS:
7.Do the same with the angle 5-O-2

19. 1
A B
2
3
O
STEPS:
8.And do the same with the angle 5-O-3
4
5

20. 1
A B
2
3
O
4
5
STEPS:
8.And do the same with the angle 5-O-3

21. 1
A B
2
3
O
STEPS:
9. Now, draw the bisector of these angles
4
5

22. 1
A B
2
3
O
4
5
STEPS:
9. Now, draw the bisector of these angles

23. 1
A B
2
3
O
4
5
STEPS:
9. Now, draw the bisector of these angles

24. 1
A B
2
3
O
4
5
STEPS:
9. Now, draw the bisector of these angles

25. 1
A B
2
3
O
STEPS:
10.To finish, draw the semicircumference to close the fan, taking as radius the distance OA=OB
4
5