Geometry unit 1.6

 Based on principles of pure geometry and may
be applied to any shape regardless of the size.
 CAD is based on geometric construction so
understanding geometric construction makes
understanding how CAD tools work easier and
increases proficiency.

Euclidian Geometry was
developed by a Roman citizen
named Euclid.
Euclid lived from approx. 330 to
260bc and wrote a 13 volume
book called Elements which
illustrated all the concepts used
in Geometric Construction

The Greeks could not do arithmetic
because:
1. They had only positive whole
numbers represented by Roman
numerals (I, II, III, IV, V)
- no negative numbers
- no fractions or decimals
-no zero

So if the line were any length other
than an even answer it could not
be solved in Roman culture.
Example: 5 / 2= 2.5
2. Had no measurement system
with units so a line could not be
measured.
As a result they had to use other
tools such as a compass and
straight edge.

 Draw constructions very lightly using
guidelines.
 Do NOT erase your guidelines- show your
work.
 Only trace over the final solution NOT the
construction.

1. Place the pivot point of the Safe-
T compass on the CP of the arc
you want to draw.
2. Hold the rotator in place with
your non-dominate hand.
3. Put the point of your pencil in an
appropriate radius hole
4. Rotate the radius arm around
the rotator by dragging your
pencil.

Begin with a given line
1. Place the compass point
on one end point (ep) of
the line.
2. Adjust the compass
radius to approximately
2/3 the length of the
line (radius must be > ½
the length of the line but
actual size does not
matter)
3. Draw an arc above and
below the line.

4. Without adjusting the
radius place the
compass point on the
opposite ep of the line .
5. Draw arcs intersecting
the first two
6. Connect the
intersections using a
straight edge.

An arc is a curved line and
is bisected using the
same steps.
Imagine a line between the
end points of the arc.
Bisect the imagined line as
you did to complete the
perpendicular bisect

Begin with a given angle
 Place the compass point on the Vertex (Q)
and adjust to a width approximately half
the length of 1 leg of the angle (exact width
is NOT important)

2. Draw an arc across each leg of
the angle
3. Move the compass point
to the intersection of one
of the legs and arc.
4. Draw an arc in the interior
of the angle.

5. Without changing the radius of
the compass do the same on the
other leg of the angle so the arcs
intersect
6. Using a straight edge connect the
vertex and intersection of the two
arcs.

Begin with a given angle
1. Draw one leg of the angle at a
new location and choose the ep
to use as the vertex

2. Place the compass point
on the vertex of the
angle
3. Draw an arc at any
convenient radius
intersecting both legs of
the angle

4. Without changing the width
of the compass place the
compass point on the ep of
the line that will be the vertex
5. Draw a similar arc intersecting the line and
extending above or below.

6. Place the point of the compass
on the intersection of the arc
and one of the legs
7. Adjust the compass so
the lead is on the other
intersection of the arc
and opposite leg .

8. Without changing the radius
of the compass place the point
on the intersection of the arc
and line at the new location
9. Draw an arc that
intersects the other arc

10. Use a straightedge to draw
a line from the vertex
through the intersection of
the 2 arcs

Begin with the 3 given
sides
1. Draw a point that will be 1 vertex of the triangle.
2. Measure one of the sides with your compass. You
will use this as the base of the triangle

3. Without changing the radius
of the compass place the
point of the compass on the
vertex point. Draw an arc to
the side of the point.
4. Draw an arc to the side
of the point.
5. Make a point on the arc.
This will be the second
vertex of the triangle

6. Using the Compass
measure the length of
one of the other given
sides
7. Without changing the
radius. Place the
compass point on one
of the two vertices and
draw an arc above or
below the base.

8. Using the Compass
the last side
9. Without changing the
radius. Place the
compass point on the
other vertex and draw
an arc that intersects
the other arc.- This
becomes the 3rd vertex.

10. Connect the 3 vertices
using a straight edge.

1. Begin by Making a point-
This will be the first
vertex
2. Using the compass
the given side and set
the compass point on
your first vertex.
3. Draw arcs to the side of the first vertex where you
want the 2nd vertex and an arc above or below to
locate the 3rd vertex

4. Place a point on one of
the two arcs- This will
be the second vertex
5. Without adjusting the
radius of the compass
place the point on the
second vertex point and
draw an arc intersecting
the first arc.

4. Connect the three
vertices using a straight
edge

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Geometry unit 1.6

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Geometry unit 1.6