Basic geometric drawing

1. DRAWING PERPENDICULAR
AND PARALLEL LINES

2. Exercise 1
Draw the perpendicular to the straight line
through the point P that is external to it

3. We have the line and the
point P, external to it
P

4. STEPS:
1.Centering at P and with an
arbitrary radius, draw an
arc that intersects the line
at points 1 and 2
P

5. P
STEPS:
1.Centering at P and with an
arbitrary radius, draw an
arc that intersects the line
at points 1 and 2

6. P
STEPS:
1.Centering at P and with an
arbitrary radius, draw an
arc that intersects the line
at points 1 and 2

7. P
STEPS:
2.Now, draw the perpendicular
bisector to the segment
whose endpoints are 1 and 2.
To do so, draw two arcs with
the same length centering the
compass at 1 and 2

8. P
STEPS:
2.Now, draw the perpendicular
bisector to the segment
whose endpoints are 1 and 2.
To do so, draw two arcs with
the same length centering the
compass at 1 and 2

9. STEPS:
3.We get the points 3 and 4.
P

10. STEPS:
4.Join the points 3 and 4,
and we obtain the
perpendicular to the
given line through point P
P

11. P
STEPS:
4.Join the points 3 and 4,
and we obtain the
perpendicular to the
given line through point P

12. P
STEPS:
4.Join the points 3 and 4,
and we obtain the
perpendicular to the
given line through point P

13. Exercise 2
Draw the perpendicular to the straight line
through the point P on it

14. We have the line and the
point P on it.
P

15. STEPS:
1.Centering at P draw an arc
with an arbitrary radius
determining points 1 and
2 equidistant from P
P

16. r
P
STEPS:
1.Centering at P draw an arc
with an arbitrary radius
determining points 1 and
2 equidistant from P

17. P
STEPS:
1.Centering at P draw an arc
with an arbitrary radius
determining points 1 and
2 equidistant from P

18. r
P
STEPS:
2.Now, draw the
perpendicular bisector
to the segment whose
endpoints are 1 and 2.
To do so, draw two arcs
with the same length
centering at 1 and 2

19. r
P
STEPS:
2.Now, draw the
perpendicular bisector
to the segment whose
endpoints are 1 and 2.
To do so, draw two arcs
with the same length
centering at 1 and 2

20. STEPS:
3.We get the points 3 and 4.
r
P

21. STEPS:
4.Join the points 3 and 4,
and we obtain the
perpendicular to the
given line on point P
r
P

22. r
P
STEPS:
4.Join the points 3 and 4,
and we obtain the
perpendicular to the
given line on point P

23. Exercise 3
Draw the perpendicular to the ray at its endpoint A

24. We have the ray with its endpoint A

25. STEPS:
1.Center your compass at the
endpoint of the ray (A). Draw an
arc with the length you want
and where this arc intersects the
ray we get the point 1.

26. STEPS:
1.Center your compass at the
endpoint of the ray (A). Draw an
arc with the length you want
and where this arc intersects the
ray we get the point 1.

27. STEPS:
2.Now, center your compass at
point 1 and with the previous
length draw another arc. Where
this last arc intersects the
previous one, we get the point 2.
2

28. STEPS:
3.Next, center your compass at
point 2 and with the same
length draw another arc (try this
time to do it longer). Where this
last arc intersects the first one,
we get the point 3.
3

29. STEPS:
4.Center your compass at point
3 and with the same length
draw another arc. Where this
arc crosses the last arc you
have drawn, we get point 4.
4

30. STEPS:
5.Join the point 4 to the given
point A and we get the
perpendicular line to the ray
on its endpoint A

31. STEPS:
5.Join the point 4 to the given
point A and we get the
perpendicular line to the ray
on its endpoint A

32. STEPS:
5.Join the point 4 to the given
point A and we get the
perpendicular line to the ray
on its endpoint A

33. Exercise 4
Draw the parallel to the given line
that passes through the point P

34. We have the line and an external
point P

35. STEPS:
1.Centering at P, draw an arc
with the radius you want
that intersects the straight
line at point N

36. STEPS:
1.Centering at P, draw an arc
with the radius you want
that intersects the straight
line at point N

37. STEPS:
1.Centering at P, draw an arc
with the radius you want
that intersects the straight
line at point N

38. N
STEPS:
1.Centering at P, draw an arc
with the radius you want
that intersects the straight
line at point N

39. STEPS:
2.Now, centering at N and
with the same radius, draw
an arc that passes through
P and intersects the
straight line at point M

40. STEPS:
2.Now, centering at N and
with the same radius, draw
an arc that passes through
P and intersects the
straight line at point M

41. STEPS:
2.Now, centering at N and
with the same radius, draw
an arc that passes through
P and intersects the
straight line at point M

42. STEPS:
3.Centre at M and draw an
arc that passes through P.
Keep this length in the
compass

43. STEPS:
3.Centre at M and draw an
arc that passes through P.
Keep this length in the
compass

44. STEPS:
3.Centre at M and draw an
arc that passes through P.
Keep this length in the
compass

45. STEPS:
4.Copy this length to the
other arc from the point N,
and you get the point R

46. STEPS:
4.Copy this length to the
other arc from the point N,
and you get the point R

47. STEPS:
4.Copy this length to the
other arc from the point N,
and you get the point R

48. STEPS:
5.Join the points P and R and
you obtain the solution,
the parallel to the given
line that passes through
the point P

49. STEPS:
5.Join the points P and R and
you obtain the solution,
the parallel to the given
line that passes through
the point P