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OPERATIONS WITH ANGLES
Exercise 1
Given the angle A, copy it onto the ray from V´
We have the angle A, that
we want to copy onto the
ray from V´
STEPS:
1.Centering at V, we draw an arc (no matter
the length you take with the compass).
You get the points 1 and 2
STEPS:
1.Centering at V, we draw an arc (no matter
the length you take with the compass).
You get the points 1 and 2
STEPS:
1.Centering at V, we draw an arc (no matter
the length you take with the compass).
You get the points 1 and 2
STEPS:
2.With the same length in the compass, we
draw the same arc from V´ getting the point 1
STEPS:
2.With the same length in the compass, we
draw the same arc from V´ getting the point 1
STEPS:
2.With the same length in the compass, we
draw the same arc from V´ getting the point 1
STEPS:
3.Now we take the distance 1-2 from the given arc and
we transport it to the new one, from the point 1
STEPS:
3.Now we take the distance 1-2 from the given arc and
we transport it to the new one, from the point 1
STEPS:
3.Now we take the distance 1-2 from the given arc and
we transport it to the new one, from the point 1
STEPS:
3.Now we take the distance 1-2 from the given arc and
we transport it to the new one, from the point 1
STEPS:
4.We get the point 2. Joining the vertex V´ and the
point 2 we obtain the angle copied.
STEPS:
4.We get the point 2. Joining the vertex V´ and the
point 2 we obtain the angle copied.
Exercise 2
Draw the bisector of the given angle A
We have the angle A and
we want to draw the
bisector of this angle
STEPS:
1.Centering at the vertex, we draw an arc
(no matter the length you take with the
compass). You get the points 1 and 2
STEPS:
1.Centering at the vertex, we draw an arc
(no matter the length you take with the
compass). You get the points 1 and 2
STEPS:
1.Centering at the vertex, we draw an arc
(no matter the length you take with the
compass). You get the points 1 and 2
STEPS:
2.Centering at each point and opening the
compass further than the middle, draw
two arcs with the same length
STEPS:
2.Centering at each point and opening the
compass further than the middle, draw
two arcs with the same length
STEPS:
2.Centering at each point and opening the
compass further than the middle, draw
two arcs with the same length
STEPS:
2.Centering at each point and opening the
compass further than the middle, draw
two arcs with the same length
STEPS:
3.Where the two arcs intersect , join it with
the vertex and you obtain the bisector of
the angle
Exercise 3
Given the following angles A, B and C, carry out
the requested operations
Exercise 3
angle A + angle B
We have to add the angle
A and the angle B
STEPS:
1.We have to copy the angle A
onto the ray as we saw
before. To do so, we are
going to draw the same arc
in all of them
STEPS:
1.We have to copy the angle A
onto the ray as we saw
before. To do so, we are
going to draw the same arc
in all of them
STEPS:
2.In the first angle, we get the
points 1 and 2
STEPS:
3.In the second angle, we get
the points 3 and 4
STEPS:
3.In the second angle, we get
the points 3 and 4
STEPS:
3.In the second angle, we get
the points 3 and 4
STEPS:
4.In the third angle, we get
the points 5 and 6
STEPS:
4.In the third angle, we get
the points 5 and 6
STEPS:
4.In the third angle, we get
the points 5 and 6
STEPS:
5.Now, we copy the first angle
onto the ray. To do it, we
draw the same arc and we
obtain the point 1. Then, on
this arc we transport the
distance 1-2 of the original
angle
STEPS:
5.Now, we copy the first angle
onto the ray. To do it, we
draw the same arc and we
obtain the point 1. Then, on
this arc we transport the
distance 1-2 of the original
angle
STEPS:
5.Now, we copy the first angle
onto the ray. To do it, we
draw the same arc and we
obtain the point 1. Then, on
this arc we transport the
distance 1-2 of the original
angle
STEPS:
5.Now, we copy the first angle
onto the ray. To do it, we
draw the same arc and we
obtain the point 1. Then, on
this arc we transport the
distance 1-2 of the original
angle
STEPS:
5.Now, we copy the first angle
onto the ray. To do it, we
draw the same arc and we
obtain the point 1. Then, on
this arc we transport the
distance 1-2 of the original
angle
STEPS:
5.Now, we copy the first angle
onto the ray. To do it, we
draw the same arc and we
obtain the point 1. Then, on
this arc we transport the
distance 1-2 of the original
angle
STEPS:
5.Now, we copy the first angle
onto the ray. To do it, we
draw the same arc and we
obtain the point 1. Then, on
this arc we transport the
distance 1-2 of the original
angle
STEPS:
7.We join the point 2 with the
vertex V´and we have the
angle A copied
STEPS:
7.Now, we have to copy the
angle B outside the angle A.
To do so, we have to take
the distance 3-4 from the
angle B and transport it
onto the same arc
STEPS:
7.Now, we have to copy the
angle B outside the angle A.
To do so, we have to take
the distance 3-4 from the
angle B and transport it
onto the same arc
STEPS:
7.Now, we have to copy the
angle B outside the angle A.
To do so, we have to take
the distance 3-4 from the
angle B and transport it
onto the same arc
STEPS:
7.Now, we have to copy the
angle B outside the angle A.
To do so, we have to take
the distance 3-4 from the
angle B and transport it
onto the same arc
STEPS:
7.Now, we have to copy the
angle B outside the angle A.
To do so, we have to take
the distance 3-4 from the
angle B and transport it
onto the same arc
STEPS:
8.The result is the space
marked in light pink color
Exercise 3
angle B – angle A
We have to substract to
the angle B, the angle A
STEPS:
1.We have to copy first the
angle B onto the ray and
then, copy the angle A
inside the angle B
STEPS:
2.We have to transport the
distance 3-4 of the angle B
onto the ray
STEPS:
2.We have to transport the
distance 3-4 of the angle B
onto the ray
STEPS:
2.We have to transport the
distance 3-4 of the angle B
onto the ray
STEPS:
2.We have to transport the
distance 3-4 of the angle B
onto the ray
STEPS:
3.Join the vertex 4
with the vertex V´
and you get the
angle B copied
STEPS:
4.Now, we have to
copy the angle A
inside the angle B.
To do so, we have
to transport the
distance 1-2 of the
angle A inside the
angle B
STEPS:
4.Now, we have to
copy the angle A
inside the angle B.
To do so, we have
to transport the
distance 1-2 of the
angle A inside the
angle B
STEPS:
4.Now, we have to
copy the angle A
inside the angle B.
To do so, we have
to transport the
distance 1-2 of the
angle A inside the
angle B
STEPS:
4.Now, we have to
copy the angle A
inside the angle B.
To do so, we have
to transport the
distance 1-2 of the
angle A inside the
angle B
STEPS:
4.Now, we have to
copy the angle A
inside the angle B.
To do so, we have
to transport the
distance 1-2 of the
angle A inside the
angle B
STEPS:
4.Now, we have to
copy the angle A
inside the angle B.
To do so, we have
to transport the
distance 1-2 of the
angle A inside the
angle B
STEPS:
5.The result of the
operation is the
space marked in
light pink color
Exercise 3
angle B + angle C – angle A
We have to do two
operations. First we have
to add the angles B and C
and then, substract with
the result, the angle A
STEPS:
1.We have to copy first the
angle B. So, we have to
transport the distance 3-4
onto the ray
STEPS:
1.We have to copy first the
angle B. So, we have to
transport the distance 3-4
onto the ray
STEPS:
1.We have to copy first the
angle B. So, we have to
transport the distance 3-4
onto the ray
STEPS:
1.We have to copy first the
angle B. So, we have to
transport the distance 3-4
onto the ray
STEPS:
2.Once we get the
angle B we have
to add it the
angle C. So, we
have to transport
the distance 5-6
outward the
angle B
STEPS:
2.Once we get the
angle B we have
to add it the
angle C. So, we
have to transport
the distance 5-6
outward the
angle B
STEPS:
2.Once we get the
angle B we have
to add it the
angle C. So, we
have to transport
the distance 5-6
outward the
angle B
STEPS:
2.Once we get the
angle B we have
to add it the
angle C. So, we
have to transport
the distance 5-6
outward the
angle B
STEPS:
2.Once we get the
addittion of the
angles B and C,
we have to
substract the
angle A to the
result.
STEPS:
3.So, we have to
transport the
distance 1-2 of the
angle A inward the
result of the
previous operation
STEPS:
3.So, we have to
transport the
distance 1-2 of the
angle A inward the
result of the
previous operation
STEPS:
3.So, we have to
transport the
distance 1-2 of the
angle A inward the
result of the
previous operation
STEPS:
3.So, we have to
transport the
distance 1-2 of the
angle A inward the
result of the
previous operation
STEPS:
3.So, we have to
transport the
distance 1-2 of the
angle A inward the
result of the
previous operation
STEPS:
3.So, we have to
transport the
distance 1-2 of the
angle A inward the
result of the
previous operation
STEPS:
4.The result is the
space marked in
light pink color

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Operations with angles

  • 2. Exercise 1 Given the angle A, copy it onto the ray from V´
  • 3. We have the angle A, that we want to copy onto the ray from V´
  • 4. STEPS: 1.Centering at V, we draw an arc (no matter the length you take with the compass). You get the points 1 and 2
  • 5. STEPS: 1.Centering at V, we draw an arc (no matter the length you take with the compass). You get the points 1 and 2
  • 6. STEPS: 1.Centering at V, we draw an arc (no matter the length you take with the compass). You get the points 1 and 2
  • 7. STEPS: 2.With the same length in the compass, we draw the same arc from V´ getting the point 1
  • 8. STEPS: 2.With the same length in the compass, we draw the same arc from V´ getting the point 1
  • 9. STEPS: 2.With the same length in the compass, we draw the same arc from V´ getting the point 1
  • 10. STEPS: 3.Now we take the distance 1-2 from the given arc and we transport it to the new one, from the point 1
  • 11. STEPS: 3.Now we take the distance 1-2 from the given arc and we transport it to the new one, from the point 1
  • 12. STEPS: 3.Now we take the distance 1-2 from the given arc and we transport it to the new one, from the point 1
  • 13. STEPS: 3.Now we take the distance 1-2 from the given arc and we transport it to the new one, from the point 1
  • 14. STEPS: 4.We get the point 2. Joining the vertex V´ and the point 2 we obtain the angle copied.
  • 15. STEPS: 4.We get the point 2. Joining the vertex V´ and the point 2 we obtain the angle copied.
  • 16. Exercise 2 Draw the bisector of the given angle A
  • 17. We have the angle A and we want to draw the bisector of this angle
  • 18. STEPS: 1.Centering at the vertex, we draw an arc (no matter the length you take with the compass). You get the points 1 and 2
  • 19. STEPS: 1.Centering at the vertex, we draw an arc (no matter the length you take with the compass). You get the points 1 and 2
  • 20. STEPS: 1.Centering at the vertex, we draw an arc (no matter the length you take with the compass). You get the points 1 and 2
  • 21. STEPS: 2.Centering at each point and opening the compass further than the middle, draw two arcs with the same length
  • 22. STEPS: 2.Centering at each point and opening the compass further than the middle, draw two arcs with the same length
  • 23. STEPS: 2.Centering at each point and opening the compass further than the middle, draw two arcs with the same length
  • 24. STEPS: 2.Centering at each point and opening the compass further than the middle, draw two arcs with the same length
  • 25. STEPS: 3.Where the two arcs intersect , join it with the vertex and you obtain the bisector of the angle
  • 26. Exercise 3 Given the following angles A, B and C, carry out the requested operations
  • 27. Exercise 3 angle A + angle B
  • 28. We have to add the angle A and the angle B
  • 29. STEPS: 1.We have to copy the angle A onto the ray as we saw before. To do so, we are going to draw the same arc in all of them
  • 30. STEPS: 1.We have to copy the angle A onto the ray as we saw before. To do so, we are going to draw the same arc in all of them
  • 31. STEPS: 2.In the first angle, we get the points 1 and 2
  • 32. STEPS: 3.In the second angle, we get the points 3 and 4
  • 33. STEPS: 3.In the second angle, we get the points 3 and 4
  • 34. STEPS: 3.In the second angle, we get the points 3 and 4
  • 35. STEPS: 4.In the third angle, we get the points 5 and 6
  • 36. STEPS: 4.In the third angle, we get the points 5 and 6
  • 37. STEPS: 4.In the third angle, we get the points 5 and 6
  • 38. STEPS: 5.Now, we copy the first angle onto the ray. To do it, we draw the same arc and we obtain the point 1. Then, on this arc we transport the distance 1-2 of the original angle
  • 39. STEPS: 5.Now, we copy the first angle onto the ray. To do it, we draw the same arc and we obtain the point 1. Then, on this arc we transport the distance 1-2 of the original angle
  • 40. STEPS: 5.Now, we copy the first angle onto the ray. To do it, we draw the same arc and we obtain the point 1. Then, on this arc we transport the distance 1-2 of the original angle
  • 41. STEPS: 5.Now, we copy the first angle onto the ray. To do it, we draw the same arc and we obtain the point 1. Then, on this arc we transport the distance 1-2 of the original angle
  • 42. STEPS: 5.Now, we copy the first angle onto the ray. To do it, we draw the same arc and we obtain the point 1. Then, on this arc we transport the distance 1-2 of the original angle
  • 43. STEPS: 5.Now, we copy the first angle onto the ray. To do it, we draw the same arc and we obtain the point 1. Then, on this arc we transport the distance 1-2 of the original angle
  • 44. STEPS: 5.Now, we copy the first angle onto the ray. To do it, we draw the same arc and we obtain the point 1. Then, on this arc we transport the distance 1-2 of the original angle
  • 45. STEPS: 7.We join the point 2 with the vertex V´and we have the angle A copied
  • 46. STEPS: 7.Now, we have to copy the angle B outside the angle A. To do so, we have to take the distance 3-4 from the angle B and transport it onto the same arc
  • 47. STEPS: 7.Now, we have to copy the angle B outside the angle A. To do so, we have to take the distance 3-4 from the angle B and transport it onto the same arc
  • 48. STEPS: 7.Now, we have to copy the angle B outside the angle A. To do so, we have to take the distance 3-4 from the angle B and transport it onto the same arc
  • 49. STEPS: 7.Now, we have to copy the angle B outside the angle A. To do so, we have to take the distance 3-4 from the angle B and transport it onto the same arc
  • 50. STEPS: 7.Now, we have to copy the angle B outside the angle A. To do so, we have to take the distance 3-4 from the angle B and transport it onto the same arc
  • 51. STEPS: 8.The result is the space marked in light pink color
  • 52. Exercise 3 angle B – angle A
  • 53. We have to substract to the angle B, the angle A
  • 54. STEPS: 1.We have to copy first the angle B onto the ray and then, copy the angle A inside the angle B
  • 55. STEPS: 2.We have to transport the distance 3-4 of the angle B onto the ray
  • 56. STEPS: 2.We have to transport the distance 3-4 of the angle B onto the ray
  • 57. STEPS: 2.We have to transport the distance 3-4 of the angle B onto the ray
  • 58. STEPS: 2.We have to transport the distance 3-4 of the angle B onto the ray
  • 59. STEPS: 3.Join the vertex 4 with the vertex V´ and you get the angle B copied
  • 60. STEPS: 4.Now, we have to copy the angle A inside the angle B. To do so, we have to transport the distance 1-2 of the angle A inside the angle B
  • 61. STEPS: 4.Now, we have to copy the angle A inside the angle B. To do so, we have to transport the distance 1-2 of the angle A inside the angle B
  • 62. STEPS: 4.Now, we have to copy the angle A inside the angle B. To do so, we have to transport the distance 1-2 of the angle A inside the angle B
  • 63. STEPS: 4.Now, we have to copy the angle A inside the angle B. To do so, we have to transport the distance 1-2 of the angle A inside the angle B
  • 64. STEPS: 4.Now, we have to copy the angle A inside the angle B. To do so, we have to transport the distance 1-2 of the angle A inside the angle B
  • 65. STEPS: 4.Now, we have to copy the angle A inside the angle B. To do so, we have to transport the distance 1-2 of the angle A inside the angle B
  • 66. STEPS: 5.The result of the operation is the space marked in light pink color
  • 67. Exercise 3 angle B + angle C – angle A
  • 68. We have to do two operations. First we have to add the angles B and C and then, substract with the result, the angle A
  • 69. STEPS: 1.We have to copy first the angle B. So, we have to transport the distance 3-4 onto the ray
  • 70. STEPS: 1.We have to copy first the angle B. So, we have to transport the distance 3-4 onto the ray
  • 71. STEPS: 1.We have to copy first the angle B. So, we have to transport the distance 3-4 onto the ray
  • 72. STEPS: 1.We have to copy first the angle B. So, we have to transport the distance 3-4 onto the ray
  • 73. STEPS: 2.Once we get the angle B we have to add it the angle C. So, we have to transport the distance 5-6 outward the angle B
  • 74. STEPS: 2.Once we get the angle B we have to add it the angle C. So, we have to transport the distance 5-6 outward the angle B
  • 75. STEPS: 2.Once we get the angle B we have to add it the angle C. So, we have to transport the distance 5-6 outward the angle B
  • 76. STEPS: 2.Once we get the angle B we have to add it the angle C. So, we have to transport the distance 5-6 outward the angle B
  • 77. STEPS: 2.Once we get the addittion of the angles B and C, we have to substract the angle A to the result.
  • 78. STEPS: 3.So, we have to transport the distance 1-2 of the angle A inward the result of the previous operation
  • 79. STEPS: 3.So, we have to transport the distance 1-2 of the angle A inward the result of the previous operation
  • 80. STEPS: 3.So, we have to transport the distance 1-2 of the angle A inward the result of the previous operation
  • 81. STEPS: 3.So, we have to transport the distance 1-2 of the angle A inward the result of the previous operation
  • 82. STEPS: 3.So, we have to transport the distance 1-2 of the angle A inward the result of the previous operation
  • 83. STEPS: 3.So, we have to transport the distance 1-2 of the angle A inward the result of the previous operation
  • 84. STEPS: 4.The result is the space marked in light pink color