1. Geometric Construction
Stephen A. Jung
Sierra College

2. Points and Lines Plane – is defined as:
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
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 Given line A-B or Arc A-B Compass Method B A
Midpoint of line
Construction circles have the same diameter and the radius is equal to more than ½ the length of the line.

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

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

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

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

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

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

15. Tangents

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

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

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

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

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

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

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

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

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

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

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

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