Geometric construction

Geometric construction

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 (360
o
)
A degree is divided into 60 minutes (60’)
A minute is divided into 60 seconds (60”)
Example: 54
o
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 180
o
.
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:?60
o

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
Circumscribed
Inscribed
Sides = 6 Sides = 6

15. Tangents

16. Drawing a Circle Tangent to a
Line
R
G
90
o
G
i
v
e
n

R
a
d
i
u
s
Given Line
Tangent Point
Center of Circle
Offset

17. Drawing a Tangent to Two Circles
Tangent Points
Tangent Points
C
1
C
2
C
1
C
2
T
T
T
T

18. Tangent to Two Arcs or Circles
C
1 C
2
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
R
G
R
D
Given Line
Required information prior to the
construction of an Arc Tangent to
a line & Arc:
Radius of the desired Arc = R
D
R
D
T
T
Given Arc
R
G
+R
D
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 = R
D
R
D
T
T
R
G
Given Arc
R
G
-R
D
R
D
Offset
Offset

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

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

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

26. Arc Tangent to Two Arcs &
Enclosing One
R
G
R
G’
Required information
prior to the
construction of an
Arc Tangent to Two
Arcs:
Radius of the
desired Arc = R
D
Given Arcs
R
D
-R
G’
R
D
+R
G
R
D
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