Geometric Construction Notes
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Table of Contents
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Geometric Construction
Introduction
Drawing Guidelines
Parts of the Safe-T
Compass
How to Use the Safe-T
Compass
Draw a Perpendicular
Bisector to a Line
Bisect an Arc
Bisect an Angle
Transfer an Angle
Construct a Triangle From
3 Sides
Construct a Equilateral
Triangle
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Geometric Construction Introduction
• 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.
Background- Euclid
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
Background- Why Didn’t
He Just Use a Ruler
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
Background- Why Didn’t
He Just Use a Ruler
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.
Drawing Guidelines
• Draw constructions very lightly using
guidelines.
• Do NOT erase your guidelines- show your
work.
• Only trace over the final solution NOT the
construction.
Safe-T Compass Review- Parts
Safe-T Compass Review- Procedure
1. Place the pivot point of the SafeT 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.
Draw a Perpendicular Bisector to a
Given Line
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.
Draw a Perpendicular Bisector to a
Given 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.
Draw a Perpendicular Bisector to a
Given Line- Solution
Summarize the Steps in Your Own
Words
Bisect an Arc
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
Summarize the Steps in Your Own
Words
Bisect Angle
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)
Bisect Angle
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.
Bisect 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.
Bisect Angle- Solution
Summarize the Steps in Your Own
Words
Transfer an Angle
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
Transfer an Angle
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
Transfer an 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.
Transfer an Angle
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 .
Transfer an Angle
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
Transfer an Angle
10. Use a straightedge to draw a
line from the vertex through
the intersection of the 2 arcs
Transfer an Angle-Solution
Summarize the Steps in Your Own
Words
Construct a Triangle Given 3 Sides
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
Construct a Triangle Given 3 Sides
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
Construct a Triangle Given 3 Sides
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.
Construct a Triangle Given 3 Sides
8. Using the Compass
measure the length of
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.
Construct a Triangle Given 3 Sides
10. Connect the 3 vertices
using a straight edge.
Construct a Triangle Given 3 SidesSolution
Summarize the Steps in Your Own
Words
Construct an Equilateral Triangle
Given 1 Side
1. Begin by Making a pointThis will be the first vertex
2. Using the compass
measure the length of 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
Construct an Equilateral Triangle
Given 1 Side
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.
Construct an Equilateral Triangle
Given 1 Side
4. Connect the three vertices
using a straight edge
Construct an Equilateral Triangle
Given 1 Side- Solution
Summarize the Steps in Your Own
Words
Summary
Identify how the exercises relate to one another:
- What do you learn from bisecting a line that you
can apply to bisecting an arc?
-
How do you use what you learned from bisecting an
arc to bisect an angle
-
How do the skills learned from bisecting an angle
help you to transfer an angle?