The document defines basic geometry concepts like points, lines, line segments, rays, and angles. It also describes common geometry tools used for technical drawing like compasses, protractors, set squares, rulers, and erasers. The bulk of the document provides step-by-step instructions for performing basic geometry constructions like copying line segments, adding and subtracting line segments, constructing perpendicular bisectors of line segments, and constructing angle bisectors. It also defines circles and related terms like circumference and center.

1. Título del libro

2. BASIC GEOMETRY CONSTRUC-
TIONS
1

3. Sección 1
CONCEPTS AND DEFINITIONS
BASIC GEOMETRY CONCEPTS AND DEFINITIONS
Geometry: is
a
branch
of
mathematics
concerned
with
questions
of
shape,
size,
relative
position
of
figures,
and
the
properties
of
space.
Point: an
entity
that
has
a
location
in
space
or
on
a
plane,
but
has
no
extent.
Line: a
concept
which
includes,
but
is
not
limited
to,
an
infinitely-­‐extended
one-­‐dimensional
figure
with
no
curvature
Line segment: It´s
a
line
with
two
end
points
Ray: a
part
of
a
line
which
is
finite
in
one
direction.
It
begins
in
a
particular
point
(initial
point)
End point: it´s
the
point
where
a
line
segment
ends
Mid point: it´s
the
point
that
is
half
way
between
the
initial
point
and
the
end
point
on
a
line
segment
Length: measurement
of
a
segment
GEOMETRY DRAWING AND SUPPLIES. CONCEPTS AND DEFINITIONS,
Freehand: It
consists
in
drawing
by
hand
without
any
guiding
indtruments.
Technical drawing: it´s
a
drawing
made
with
the
help
of
instruments
or
supplies.
Compass: is
a
tool
for
drawing
arcs
and
circumferences
and
also
for
measuring
lengths.
It
has
two
arms
linked
by
a
hinge
Protactor: It
is
an
instrument
used
to
measure
or
to
draw
angles
on
paper.
Set triangles (US) or set square (UK): they
are
two
tools
with
a
triangular
shape.
One
is
caled
the
45º
triangle
(or
the
45º
square)
and
the
other
the
30º
or
60
º
triangle
or
square.
Both
of
them
have
a
90º
angle.
Using
both
of
them
at
the
same
time
you
can
draw
parallel
and
perpendicular
lines,
and
different
angles
measumerement.
2

4. Eraser: it
is
an
object
used
to
delete
on
the
paper
Marker or felt-tip pen: it
is
a
pen
which
has
its
own
ink-­‐source,
and
usually
a
tip
made
of
porous,
pressed
fibers.
Ruler: it
is
an
instrumemnt
used
to
draw
straight
lines
or
to
measure
the
distance
between
two
points.
3
TIP: Visit http://mathisfun.com/geometry/constructions.html
CONSTRUCTIONS

5. 4

6. 5

7. Sección 2
CONSTRUCTIONS
1. OPERATIONS WITH LINE SEGMENTS
The
purpose
of
this
section
is
to
perform
some
operations
with
line
segments.
It
is
very
important
that
you
always
use
the
compass
to
take
lenghts,
to
copy
or
to
move
them.
You
don´t
need
the
ruler
fot
anything
but
to
draw
the
rays.
a) Line
segment
copying:
Given
the
segment
AB,
copy
it.
It
must
have
the
same
lenght.
STEP
1:
Draw
a
ray
from
point
A.
You
can
place
point
1
wherever
you
want
b) Line
segment
addition:
Given
the
line
segments
AB,
CD
and
EF,
add
them.
Eraser:
it
is
an
object
used
to
dele-­‐
te
on
the
paper
6
1
STEP
2:
Using
the
compass
take
the
lenght
AB2
STEP
2:
Using
the
compass,
take
AB
lenght,
adn
copy
it
on
ray
from
A´.
You
obtain
point
B´.
3 STEP
3:
Keep
that
length
in
your
compass,
set
it
on
the
beginning
of
the
ray
(point
A´)
and
draw
an
arc
obtaining
B´.
4 STEP
4:
Finally
enhance
with
black
ink
the
result
A´B´.
STEP
1:
Draw
a
ray
from
point
A´

8. STEP
3:
Take
CD
length
with
the
compass,
and
copy
it
from
point
B´.
You
obtain
point
C´.
STEP
4:
Repeat
step
2
or
step
3
using
EF
lenght
and
point
D´.
You
obtain
point
F´.
STEP
5:
The
result
is
the
total
length
of
the
three
segments
copied
one
after
the
other.
Remembre
to
enhance
the
result
with
black
ink.
c) Line
segment
substraction:
Given
the
line
segments
AB,
CD
substract
them.
STEP
1:
Draw
a
ray
from
point
A´
STEP
2:
Using
the
compass,
take
AB
lenght,
adn
copy
it
on
ray
from
A´.
You
obtain
point
B´.
STEP
3:
Take
CD
length
with
the
compass,
and
copy
it
from
point
A´
(or
C´).
You
obtain
point
D´.
STEP
4:
The
result
of
AB-­‐CD
is
seg-­‐
ment
D´B´.
You
must
enhance
it
with
black
ink.

9. 2. PERPENDICULAR SEGMENT LINE BISECTOR
Draw
the
perpendicular
segment
line
bisector
when
you
know
the
segment
AB.
3. ANGLE BISECTOR
8
STEP
1:
Draw
two
arcs
with
the
sa-­‐
me
radius
using
points
A
an
B
(cen-­‐
ter
os
the
arcs).
You
will
get
points
1
and
2
where
both
arcs
intersect
STEP
2:
Join
point
1
and
point
2
and
you
will
get
the
perpendicular
segment
line
bisector
STEP
1:
Make
an
arc
cen-­‐
tered
in
point
V
with
the
radius
you
want
STEP
2:
Centered
in
the
points
1
and
2,
with
the
same
radius,
draw
two
arcs.
They
intersect
in
point
3.
STEP
3:
Join
point
3
with
point
V
and
you
will
ob-­‐
tain
the
angle
bisector

10. 2. CIRCLES
Circle: set
of
points
equidistant
to
a
point
called
center
Circumference:
total
length
of
the
circle
Center:
point
equidistant
to
any
point
on
the
circle
Radius:
distance
between
the
circunference
an
the
center
Diameter: Line
segment
that
passes
through
the
center
and
connects
two
points
of
the
circunference
Chord:
line
segment
that
joins
two
points
of
the
circunference
(
it
doesn´t
pass
through
the
center)
Tangent:
line
that
intersects
the
circumference
in
one
point
Outer circle:
circle
that
is
outside
the
circumference
HOW TO DRAW A CIRCLE KNOWN THREE POINTS (A,B,C)
9
STEP
1:
Join
point
A
with
point
B.
Trace
its
perpendicular
bisector.
STEP
2:
Join
points
B
and
C
(or
A
and
C).
Trace
its
perpendicular
bisector.
Both
perpendicular
bisector
inter-­‐
sect
in
the
center
of
the
circle.
STEP
3:
Draw
the
circumference
with
the
centre
in
that
point
and
radius
to
any
of
the
given
points.

11. 10

12. 11
A
B
C
DRAW
THE
CIRCLE
GIVEN
THREE
POINTS
OF
ITS
CIRCUMFERENCE
A
BC
DRAW
THE
CIRCLE
GIVEN
THREE
POINTS
OF
ITS
CIRCUMFERENCE

13. 12
ADD
THESE
SEGMENTS
B
SUBSTRACT
THESE
SEGMENTS
B
DIVIDE
THIS
SEGMENT
IN
5
PIECES:
you
have
to
use
THALES
A
C D
A
C D
C D

14. 13
MAKE
THESE
OPERATIONS
WITH
KNOWING
THESE
SEGMENTS
A
C D
B E F
A)
AB + CD
4
C)
1
2
AB +
3
4
CD −
1
5
EFC)
1
2
AB + 2
4
CD − 1
3
EF
CD
6

15. 14
CIRCLES
PATTERN

16. 15
DRAW
A
PENTAGON
WITH
SIDE=65
CM

17. 16
DRAW
A
CIRCUMFERENCE
WITH
RADIUS
R=5
CM
AND
IN
IT,
AN
HEXAGON

18. 17
DRAW
THE
STAR
SHAPE
IN
A
HEPTAGON.
THE
HEPTAGON
IS
INSIDE
A
CIRCLE
WHICH
HAS
A
5
CM
RADIUS

19. 18
DRAW
THE
STAR
SHAPE
IN
A
DECAGON.
THE
HEPTAGON
IS
INSIDE
A
CIRCLE
WHICH
HAS
A
4
CM
RADIUS

20. 19

21. 20
DRAW A PENTAGON. SIDE = 6 CM
DRAWING
NumberAUTHOR Class Date Score
PROJECT

22. 21
DRAW A 6 CM SIDE HEXAGON
DRAWING
NumberAUTHOR Class Date Score
PROJECT

23. 22
DRAWING
NumberAUTHOR CLASS Date Score
PROJECT
DRAW A HEPTAGON. SIDE LENGHT 5 CM

24. 23
DRAWING
NumberAUTHOR Class Date Score
PROJECT
DRAW A 4 CM LENGHT SIDE OCTAGON

25. 24
NumberAUTHOR Class Date Score
DRAWINGPROJECT
DRAW A 4CM LENGHT 9 SIDES POLYGON

26. 25
DRAW A DECAGON (SIDE LENGHT=4 CM) AND DRAW ALL ITS POSSIBLE STAR SHAPES
DRAWING
NumberAUTHOR Class Date Score
PROJECT

27. 26
DRAW A DECAGON (10 SIDES; L=4CM) AND ITS STAR SHAPE POLYGON. GIVE IT A 6 CM WIDTH.
DRAWING
NumberAUTHOR Class Date Score
PROJECT

28. 27
DRAW A 11 SIDES POLYGON WITH L=4CM AND ONE OF ITS STAR SHAPES. GIVE IT A 6 CM WIDTH.
DRAWING
NumberAUTHOR Class Date Score
PROJECT

29. 28
DRAWING
NumberAUTHOR Class Date Score
PROJECT