This document provides an overview of geometric constructions. It defines basic geometric elements like points, lines, planes, angles and their properties. It then describes how to construct common geometric shapes like triangles, quadrilaterals, polygons, circles and arcs using compass and straightedge. Specific techniques are presented for drawing shapes given certain parameters, finding bisecting lines and angles, transferring angles, constructing tangents and tangent arcs.

1. Geometric
Construction
Stephen A. Jung
Sierra College

2.  Point – represents a location in space or on a drawing
 No height, width, or depth
 Represented by the intersection of two lines
 Short cross bar on a line, or
 A small point element e.g. ( + x l )
 Line – is defines as “that which has length without width”1
 Straight Line is the shortest distance between two points
 Lines can be:
 Parallel – symbol = ll
 Perpendicular – symbol =
 Plane – is defined as:
 3 points in a space
 1 point and an entity with end points e.g. line or arc
Points and Lines
1 Defined by Euclid

3. Angles
 Angles are formed by two intersecting
lines
 Common symbol = a
 360 Degrees in a full circle (360o
)
 A degree is divided into 60 minutes (60’)
 A minute is divided into 60 seconds (60”)
 Example: 54o
43’ 28” is read 54 degrees, 43
minutes, and 28 seconds.
 Different kinds of angles are:

4. Triangles
 A triangle is a plane figure bounded by
three straight lines and the sum of the
interior angles is always 180o
.
 Types of triangles:

5. Quadrilaterals
 A quadrilateral is a plane figure bounded
by four straight sides.
 If the opposite sides are parallel, the
quadrilateral is also a parallelogram.

6. Polygons
 A polygon is any plane figure bounded by
straight lines.
 If the polygon has equal angles and equal sides,
it can be inscribed or circumscribed around a
circle, an is called a regular polygon.

7. Circles and Arcs
 A circle is a closed curve with all points
the same distance from a point called the
center.
 Attributes of a circle:

8. Bisecting a Line or Arc
B
A
Construction circles have the same
diameter and the radius is equal to
more than ½ the length of the line.
Given line A-B or Arc A-B
Compass Method
Midpoint of line

9. Bisecting an Angle
Given angle A-B-C
Compass Method
A
C
B
Initial construction circle drawn at any convenient radius.
Second and third circles radius equal to first.
Bisector
Equal Angles
R

10. Transferring an Angle
Compass Method
X
Z
Y
Initial construction circle drawn at any convenient radius.
Second circle radius (R’) equal to first
circle radius (R).
Y’New Location
Given Angle
X-Y-Z
R
R=R’
X’
R’
r
r’
Z’
r=r’
Equal Angles
Equal Angles

11. Drawing a Triangle with sides given.
Measure length of each side given.
D
F
E
D
E
F
Construct circles from end points of base.
ED

12. Drawing a Right Triangle with
only two sides given
Measure length of each side given.
M
N
R=M R= 1/2 N
N
Construct a circle = M from one end point of base.
M
Construct base segment N.

13. Drawing an Equilateral Triangle
R
Given Side
S
R R
Measure length of side given.
Draw construction circles from the end points of
the given side with the radius equal to that length.
All angles are equal to:? 60o

14. Drawing Regular Polygons
using CAD
Required information prior to the construction of a polygon:
1. Number of sides
2. Center location
3. Radius of the polygon
4. Inscribed in a circle or Circumscribed about a circle
R R
CircumscribedInscribed
Sides = 6 Sides = 6

15. Tangents

16. Drawing a Circle Tangent to a
Line
R
G
90
o
GivenRadius
Given Line
Tangent Point
Center of Circle
Offset

17. Drawing a Tangent to Two Circles
Tangent Points
Tangent Points
C1
C2
C1
C2
T
T
T
T

18. Tangent to Two Arcs or Circles
C1 C2
Only One Tangent Point

19. Drawing a Tangent Arc in a
Right Angle
Required information prior to the
construction of an Arc Tangent to a line:
1. Radius of the desired Arc = R
R
R
R
Given Right Angle
Offset
Offset

20. Drawing Tangent Arcs:
Acute & Obtuse Angles
R
R
R
R
R
T
T
T
T
Acute Angle
Obtuse Angle
R
Required information prior to
the construction of an Arc
Tangent to a line:
Radius of the desired Arc = R
Acute Angle Example
Obtuse Angle Example
Offset
Offset
Offset
Offset

21. Arc Tangent to:
an Arc and a Straight Line
RG
RD
Given Line
Required information prior to the
construction of an Arc Tangent to
a line & Arc:
Radius of the desired Arc = RD
RD
T
T
Given Arc
RG+RD
Offset
Offset

22. Arc Tangent to:
an Arc and a Straight Line
Given Line
Required information prior to
the construction of an Arc
Tangent to a line & Arc:
Radius of the desired Arc = RD
RD
T
TRG
Given Arc
RG-RD
RD
Offset
Offset

23. Arc Tangent to two Arcs
Given Arcs
RG’
RG
Required information prior to
the construction of an Arc
Tangent to a line & Arc:
Radius of the desired Arc = RD
T
T
RD
RG+RD RG’+RD
Offset Offset

24. Arc Tangent to two Arcs
cont.
RG’
RG
Required information prior to
the construction of an Arc
Tangent to Two Arcs:
Radius of the desired Arc = RD
Given Arcs
T
T
RD
RG+RD
RG’-RD
Offset
Offset

25. Arc Tangent to Two Arcs
cont. Enclosing Both
RG
RG’
Required
information prior
to the construction
of an Arc Tangent
to Two Arcs:
Radius of the
desired Arc = RD
T
T
Given Arcs
RD-RG
RD-RG’
RD

26. Arc Tangent to Two Arcs &
Enclosing One
RG
RG’
Required information
prior to the
construction of an
Arc Tangent to Two
Arcs:
Radius of the
desired Arc = RD
Given Arcs
RD-RG’
RD+RG
RD
T
T
Offset

27. That’s All Folks!

28. Tangent Arcs – Obtuse Angles
Example

29. Tangent Arcs – Acute Angles
Example

30. Circles and Arcs

31. Polygons

32. Quadrilaterals

33. Triangles

34. Angles

35. Points and Lines