Basic operations review

Exercise 1
Draw the perpendicular bisector of the line segment AB
and mark its midpoint M
___

STEPS:
1.Center your compass
at point A, open it
further from the
middle of the
segment AB, and
draw an arc.

STEPS:
2.Do the same from
point B, where
these arcs cross
each other we get
points 1 and 2.

STEPS:
3.Join 1 and 2, and this
way we will get the
perpendicular bisector
of segment AB.

STEPS:
3.Join 1 and 2, and this
way we will get the
perpendicular bisector
of segment AB. Where
the perpendicular
bisector crosses the
line segment AB, we
get the midpoint M.
M

Exercise 2
Divide the line segment AB into 5 equal parts
___

We have the segment AB
that we want to divide.
We are going to divide it
into 5 parts.

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

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

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

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

1
2
3
r
4
STEPS:
2.Choose a measure
you want with
your compass and,
from point A, draw
arcs with this
measure on the
oblique ray. You
have to draw
as many arcs as
parts you want
to divide the
segment

r
1
2
3
4
5
STEPS:
2.Choose a measure
you want with
your compass and,
from point A, draw
arcs with this
measure on the
oblique ray. You
have to draw
as many arcs as
parts you want
to divide the
segment

r
1
2
3
4
5
STEPS:
3.Join the last point of the
oblique ray, 5, with the
endpoint B.

r
1
2
3
4
5
STEPS:
4.Using your set square, draw
parallels to the segment 5B
(it determines the direction
to draw parallels) from
each division on the ray.

r
1
2
3
4
5
STEPS:
5.The result is the segment
AB divided into five parts.
In the exercise we have
divided the segment into
five parts, but you can
divide the segment into as
many parts as you need.

Exercise 3
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:
2.Centering at each point and opening the compass further
than half the distance between the points 1 and 2 , draw
two arcs with the same length

STEPS:
3.Draw a line joining the vertex with the point where
the two arcs intersect and you obtain the bisector of
the angle

Exercise 4
Given the following angles A, B and C, carry out
the requested operations

To add the angles, first of all we have to transport them onto the ray. To make the
resolution of the exercises easier, we are going to draw the same arc on all the
angles and also on all the rays where we are going to carry out the operations. We
start with angle A

We draw an arc on angle A, centering the compass at V

The arc intersects with the sides of the angle at point 1 and 2

We also draw the same arc on all the rays where we
are going to carry out the operations

On the ray where we are going to add up the angles

On the ray where we are going to subtract the angles

And on the ray where we are going to add and
subtract the angles

And on the ray where we are going to add and
subtract angles

angle A + angle B
Once we have finished drawing the same arc on all the angles and on all the rays, we start
with the first operation:

STEPS:
1.We name the intersection
point of the arc on the ray
with the number 1 because
we are going to place the
distance 1-2 of the angle A,
starting at this point

STEPS:
1.We take the distance 1-2
with the compass

STEPS:
1.And we transport it onto the
arc, drawn on the ray,
starting at point 1

STEPS:
1.We join the vertex with point 2
and we have the angle A copied

STEPS:
2.Now we have to copy the other
angle (angle B) by the side of
the first one (angle A). So, the
point 2 is going to become the
point 3 of the angle B

STEPS:
2.We take the distance 3-4 from
the angle B and we transport it
onto the arc, starting at point 3

STEPS:
2.As we are adding, we draw the
angle B outwards

STEPS:
3.We get the point 4. We draw a
straight line joining the vertex V´
with point 4 and we obtain the
angle B copied

STEPS:
4.The result of the addition is a
straight angle, defined by the grey
colour and the two sides of the
angle, highlighted in red

STEPS:
1.We have to copy first the
angle B. So, we name the
intersection point of the arc
on the ray with the number
3 because we are going to
place the distance 3-4 of the
angle B, starting at this
point

STEPS:
1.We take the distance 3-4
with the compass

STEPS:
1.We transport it onto the arc,
drawn on the ray, starting at
point 3

STEPS:
1.We join the vertex V´with point 4 and we
have the angle B copied

STEPS:
1.Now we have to copy the other angle (angle A) by the side of the first
one (angle B). So, the point 4 is going to become the point 1 of the
angle A

STEPS:
2.We take the distance 1-2 from the angle A and we transport it onto the arc,
starting at point 1

STEPS:
2.As we are
subtracting, we
have to draw the
angle A inwards,
not outwards

STEPS:
2.We get the point 2.
We draw a straight
line joining the
vertex V´with point
2 and we obtain the
angle A copied, over
the angle B

STEPS:
3.The result of the
subtraction is an
acute angle, defined
by the grey colour
and the two sides of
the angle, highlighted
in red

(angle B + angle C) – angle A

STEPS:
1.First of all, we have to add
up the angles B and C and to
this result, we have to
subtract the angle A

STEPS:
1.To add up the angles B and
C, we have to copy first the
angle B. So, we name the
intersection point of the arc
on the ray with the number
3 because we are going to
place the distance 3-4 of the
angle B, starting at this
point

STEPS:
1.We join the vertex V´ with point 4 and we
have the angle B copied

STEPS:
1.Now we have to copy the other angle (angle C) by the side of the first one (angle
B). So, the point 4 is going to become the point 5 of the angle C

STEPS:
2.We take the distance 5-6 from the angle C and we transport it onto the
arc, starting at point 5

STEPS:
2.As we are adding,
we have to draw
the angle C
outwards

STEPS:
3.We get the point 6. We draw a straight line joining the vertex V´
with point 6 and we obtain the angle C copied

STEPS:
3.So, the result of the addition would be these two angles together. Now, we
have to subtract to this addition the angle A. To do the subtraction, the point
6 become the point 1 because we need to transport the distance 1-2 of the
angle A on the arc of the ray, starting at point 1

STEPS:
4.We take the distance 1-2 from the angle A and we transport it onto
the arc, starting at point 1

STEPS:
4.As we are
subtracting, we
have to draw the
angle A inwards,
not outwards

STEPS:
4.We get the point 2.
We draw a straight
line joining the vertex
V´with point 2 and we
obtain the angle A
copied, over the result
of the addition of B+C

STEPS:
5.The result of the
operation (B+C)-A is a
right angle, defined
by the grey colour
and the two sides of
the angle, highlighted
in red

Basic operations review

More Related Content

What's hot

Similar to Basic operations review

More from Cnavarrovargas

Recently uploaded

Basic operations review