1. LINE SEGMENT OPERATIONS

2. In geometry, a line segment is a part of a line that is bounded by
two distinct endpoints, and contains every point on the line
between its endpoints. Line segments are generally labeled with
two capital letters corresponding to their endpoints.

3. 1. LINE SEGMENT COPYING

4. Start with a line
segment AB that we
will copy.

5. STEPS:
1.Draw a ray from point A´.
r

6. STEPS:
2.With the compass
take the length AB.
r

7. STEPS:
3.With the length AB kept with
the compass set the center on
the ray´s point A´ and draw an
arc obtaining B´.
B´ r

8. r
STEPS:
3.With the length AB kept with
the compass set the center on
the ray´s point A´ and draw an
arc obtaining B´.

9. 2. LINE SEGMENTS ADDITION

10. Given the line segments AB and CD,
we have to add them up.

11. STEPS:
1.Draw a ray from the point A´.
r

12. STEPS:
2.With the compass take the
length AB and copy it on the
ray from A´, obtaining B´.
r

13. STEPS:
2.With the compass take the
length AB and copy it on the
ray from A´, obtaining B´.
r

14. STEPS:
2.With the compass take the
length AB and copy it on the
ray from A´, obtaining B´.
r

15. STEPS:
3.We take the length CD and
copy it on the ray from B´
obtaining the segment C´D´.
r

16. STEPS:
3.We take the length CD and
copy it on the ray from B´
obtaining the segment C´D´.
r

17. STEPS:
3.We take the length CD and
copy it on the ray from B´
obtaining the segment C´D´.
r

18. STEPS:
3.We take the length CD and
copy it on the ray from B´
obtaining the segment C´D´.
r

19. STEPS:
4.The solution is the segment
A´D´.
r

20. 3. LINE SEGMENTS SUBTRACTION

21. Given the line segments AB and
CD, we have to construct a
segment whose length is the
difference of both of them.

22. STEPS:
1.Draw a ray from the
point A´.

23. STEPS:
1.Take with the compass the
AB length, the longest one,
and copy it on the ray from
A´, obtaining B´ (AB line
segment copying).

24. STEPS:
1.Take with the compass the
AB length, the longest one,
and copy it on the ray from
A´, obtaining B´ (AB line
segment copying).

25. STEPS:
1.Take with the compass the
AB length, the longest one,
and copy it on the ray from
A´, obtaining B´ (AB line
segment copying).

26. STEPS:
2.Take with the compass the
length CD, the smallest
one, and copy it on the ray
from A´, obtaining C´D´.

27. STEPS:
2.Take with the compass the
length CD, the smallest
one, and copy it on the ray
from A´, obtaining C´D´.

28. STEPS:
2.Take with the compass the
length CD, the smallest
one, and copy it on the ray
from A´, obtaining C´D´.

29. STEPS:
1.The differences of
length, length from D´
to B´, is the result.

30. 4. LINE SEGMENT MULTIPLICATION

31. Given a segment AB we
have to construct a
segment 3 times longer
than AB.

32. STEPS:
1. Draw a ray from the point A´.

33. STEPS:
1. With the compass take the
length AB and copy it on
the ray from A´.

34. STEPS:
1. With the compass take the
length AB and copy it on
the ray from A´.

35. STEPS:
2.Repeat the operation three
times.

36. STEPS:
2.Repeat the operation three
times.

37. STEPS:
3.The result is the segment
A´B´ which is three times as
long as AB.

38. 5. DIVIDING A SEGMENT INTO SEVERAL EQUAL PARTS

39. Draw the given segment
AB. This is the segment
that we want to divide.
We are going to divide it
into 3 parts.

40. STEPS:
1.From point A draw an
oblique ray (r). It doesn´t
matter the angle you take.
r

41. r
1
STEPS:
2.Choose a measure with your
compass and from point A
draw arcs on the oblique ray.
You have to draw as many arcs
as parts you need.

42. r
1
2
STEPS:
2.Choose a measure with your
compass and from point A
draw arcs on the oblique ray.
You have to draw as many arcs
as parts you need.

43. r
1
2
3
STEPS:
2.Choose a measure with your
compass and from point A
draw arcs on the oblique ray.
You have to draw as many arcs
as parts you need.

44. STEPS:
3.Join the last point of the
oblique ray, 3, with point B.
r
1
2
3

45. STEPS:
4.Draw parallels using your
set square to the segment
3B from the other points on
the ray.
r
1
2
3

46. r
1
2
3
STEPS:
4.Draw parallels using your
set square to the segment
3B from the other points on
the ray.

47. r
1
2
3
STEPS:
4.Draw parallels using your
set square to the segment
3B from the other points on
the ray.

48. r
1
2
3
STEPS:
5.The result is the segment
AB divided into three parts.
Here we have divided the
segment into three parts,
but you can divide the
segment into as many parts
as you need.

49. r
STEPS:
5.The result is the segment
AB divided into three parts.
Here we have divided the
segment into three parts,
but you can divide the
segment into as many parts
as you need.