2. Section 2 Drafting Techniques and Skills
Chapter 6
Basic Geometric Constructions
Section 2 Drafting Techniques and Skills

3. Objectives
Use manual drafting tools and methods to make geometric constructions.
Use CAD commands and methods to make geometric constructions.
Draw, bisect, and divide lines.
Construct, bisect, and transfer angles.
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4. Objectives Draw triangles, squares, hexagons, and octagons.
Use special techniques to construct regular polygons.
Construct circles and arcs.
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5. Geometric Constructions
Widely used in drafting.
Based on principles of plane geometry.
Proper instruments required in manual work.
Most efficient methods should be used in CAD work.
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6. Constructions for Straight Lines
Bisecting lines
Drawing parallel lines
Drawing perpendicular lines
Dividing lines
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7. Bisect a Line Strike arcs using endpoints of Line EF as centers.
Use equal radii greater than one-half Line EF.
Draw Line GH through arc intersections.
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8. Bisect a Line Enter Line command and enter Midpoint object snap.
Pick near midpoint of Line AB.
Draw line in any direction.
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9. Draw a Line Through a Point and Parallel to a Given Line
Position T-square and triangle to align with Line AB.
Slide triangle to align with Point P.
Draw Line CD through Point P.
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10. Draw a Line Through a Point and Parallel to a Given Line
Enter Line command and pick Point C as first point.
Enter Parallel object snap and acquire point along Line AB.
Draw Line CD along alignment path.
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11. Draw a Line Through a Point and Perpendicular to a Line
Strike arcs using arbitrary radius and Point P as center.
Strike arcs where arcs intersect Line DE using same radius.
Draw Line PH.
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12. Draw a Line Through a Point and Perpendicular to a Line
Enter Line command and specify Point P as first point.
Enter Perpendicular object snap and snap to Line AB to draw line.
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13. Divide a Line Into a Given Number of Equal Parts
Draw vertical line at Point B (Line BC).
Place scale so that 11 equal divisions are between Point A and Line BC.
Mark points and project them parallel to Line BC on Line AB.
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14. Divide a Line Into Proportional Parts
Draw vertical line at Point B (Line BC).
Place scale so that nine equal divisions are between Point A and Line BC.
Mark proportional divisions and project them parallel to Line BC on Line AB.
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15. Divide a Line Into a Given Number of Equal Parts
Enter Divide command and select Line AB.
Specify number of divisions (seven).
Change point style to display markers if needed.
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16. Constructions for Angles
Bisecting angles
Transferring angles
Drawing perpendiculars
Laying out angles
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17. Angle Symbols and Types of Angles
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18. Bisect an Angle Strike Arc D using arbitrary radius.
Strike arcs from intersections of arcs and the angle.
Draw Line AE where new arcs intersect.
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19. Bisect an Angle Enter Line command and pick Point A as first point.
Enter Mid Between Points object snap.
Pick Point B and then Point C to draw the bisector.
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20. Transfer an Angle Strike equal arcs from Points A and A.
Draw arc from Point E to intersect Point F.
Draw arc with same radius from Point E.
Draw Line AC.
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21. Transfer an Angle
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22. Draw a Perpendicular Lay off three equal segments on Line AB.
Strike Arc C with radius of four units and center at Point B.
Strike Arc D with radius of five units and center at Point A.
Draw perpendicular where arcs intersect.
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23. Draw a Perpendicular
Enter Line command and activate Perpendicular object snap.
Pick near end of given line.
Specify second point of line.
Ortho mode is quicker if given line is horizontal or vertical.
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24. Lay Out a Given Angle
Align protractor on Line AB to mark desired angle (35).
Draw line from vertex indicator (Point C) to Point D.
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25. Lay Out a Given Angle
Enter Line command and use polar coordinates to draw inclined line at 60.
Specify Point C as first point.
as second point.
Polar tracking and direct distance entry allow for specific distance.
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26. Polygon and Regular Polygon Types
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27. Construct a Triangle with Three Sides Given
Lay off one side (Side C) and arc with radius equal to one side.
Lay off arc with radius equal to remaining side.
Draw sides.
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28. Construct a Triangle with Three Sides Given
Draw Side C.
Draw circle with radius equal to Arc A and center at endpoint of line.
Draw circle with radius equal to Arc B intersecting first circle.
Draw remaining sides.
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29. Construct a Triangle with Two Sides and Included Angle Given
Lay off Side B.
Construct angle at one endpoint.
Strike arc with radius equal to Side A.
Join endpoints of lines.
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30. Construct a Triangle with Two Sides and Included Angle Given
Draw Side B.
Draw Side A using polar coordinates or tracking.
Draw remaining side.
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31. Construct a Triangle with Two Angles and Included Side Given
Lay off Side AB.
Construct Angles A and B at ends of Line AB.
Extend lines to their intersection.
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32. Construct a Triangle with Two Angles and Included Side Given
Draw Side AB.
Draw inclined lines for Angles A and B using polar coordinates or tracking.
Enter Trim command and trim lines to their intersection.
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33. Construct an Equilateral Triangle
Lay off given side (Side AB).
Strike two arcs with radii equal to side and centers at Points A and B.
Draw remaining sides where arcs meet.
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34. Construct an Equilateral Triangle
Draw Side AB.
Enter Polygon command and specify three sides.
Enter Edge option, select endpoint, and specify side length and direction.
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35. Construct an Isosceles Triangle
If base and side lengths are known, use triangle method for three side lengths.
If two angles and one side length are known, use triangle method for two angles and included side length.
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36. Construct a Right Triangle
If lengths of two sides forming 90 angle are known, construct perpendicular.
Join ends to form hypotenuse.
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37. Construct a Right Triangle with Hypotenuse and One Side Given
Draw hypotenuse (Line AB).
Draw semicircle with radius equal to one-half Line AB.
Strike Arc AC equal to other given side.
Draw Lines AC and BC.
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38. Construct a Right Triangle with Hypotenuse and One Side Given
Draw hypotenuse (Line AB).
Draw circle with midpoint of Line AB as center and radius equal to one-half Line AB.
Draw circle with radius equal to other given side.
Draw Lines AC and BC.
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39. Construct a Square with One Side Given
Lay off one side (Line AB).
Draw three perpendicular lines (Lines BC, CD, and AD) to correct length.
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40. Construct a Square with One Side Given
Draw Side AB.
Enter Polygon command and specify four sides.
Enter Edge option, select endpoint, and specify side length and direction.
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41. Construct a Square with Diagonal Given
Draw circle with radius equal to half of diagonal.
Draw 45 lines across center.
Join points where inclined lines intersect circle.
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42. Construct a Square with Diagonal Given
Enter Polygon command and specify four sides.
Pick center point.
Enter Inscribed option and specify center radius as one-half the diagonal.
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43. Construct a Regular Pentagon with Side Length Given
Draw Side AB.
Construct 108 angle at Point B at distance of Side AB.
Draw remaining sides in same manner.
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44. Construct a Regular Pentagon with Side Length Given
Enter Polygon command and specify five sides.
Enter Edge option and select endpoint.
Enter side length.
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45. Construct an Inscribed Pentagon with Radius Given
Draw circle of given radius and bisect radius.
Strike Arcs HD, DJ, and DC.
Strike Arcs EA and CB.
Draw lines between intersection points.
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46. Construct an Inscribed Pentagon with Radius Given
Enter Polygon command and specify five sides.
Pick center point.
Enter Inscribed option and specify given radius.
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47. Construct a Hexagon with Distance across Flats Given
Draw circle equal in diameter to given distance.
Draw lines tangent to circle.
Draw remaining sides.
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48. Construct a Hexagon with Distance across Flats Given
Enter Polygon command and specify six sides.
Pick center point.
Enter Circumscribed option and specify radius as half the given distance.
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49. Construct a Hexagon with Distance across Corners Given
Draw circle equal in diameter to given distance.
Draw 60 lines across center.
Join intersection points.
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50. Construct a Hexagon with Distance across Corners Given
Enter Polygon command and specify six sides.
Pick center point.
Enter Inscribed option and specify radius as half the given distance.
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51. Construct an Octagon with Distance across Flats Given
Draw circle equal in diameter to given distance.
Draw sides tangent to circle.
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52. Construct an Octagon with Distance across Corners Given
Draw circle equal in diameter to given distance.
Draw 45 lines across center.
Join intersection points.
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53. Construct an Octagon Enter Polygon command and specify eight sides.
Pick center point.
Use Circumscribed option if distance across flats is known.
Use Inscribed option if distance across corners is known.
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54. Construct an Inscribed Regular Polygon with Circle Diameter Given
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55. Construct a Regular Polygon with Side Length Given
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56. Transfer and Rotate a Plane Figure
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57. Transfer and Rotate a Plane Figure
Draw Line AB in desired orientation.
Enter Rotate command. Use Copy, Reference, and Points options to copy and rotate polygon.
Relocate polygon. Erase Line AB drawn in Step 1.
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58. Duplicate a Plane Figure with Irregular Curves
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59. Duplicate a Plane Figure with Irregular Curves
Enter Copy command and select entire object or individual entities.
Select base point.
Specify second point.
Different selection methods can be used to simplify operation if selecting individual objects.
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60. Enlarge or Reduce a Plane Figure Using Grid Squares
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61. Enlarge or Reduce an Object
Enter Scale command and select object.
Select base point.
Enter scale factor.
Use Copy option if duplicating object.
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62. Circle and Arc Constructions
Circles have center, diameter, and radius.
Irregular curve constructions common in drafting.
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63. Construct a Circle Through Three Given Points
Draw and bisect Lines AB and BC.
The center of circle is intersection of bisectors.
The radius equals distance from intersection to any point.
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64. Locate the Center of a Circle or Arc
Draw two nonparallel chords.
Bisect each chord.
Center of circle or arc is intersection of bisectors.
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65. Construct a Circle Through Three Points
Enter Circle command.
Enter Three Points option.
Select three points individually.
To locate center point of arc or circle, use Center object snap.
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66. Construct a Circle Within a Square
Draw 45 diagonals to locate center.
Locate midpoint of one side of square (Point E).
The radius equals distance from center to Point E.
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67. Construct a Circle Within a Square
Enter Circle command.
Enter Two Points option.
Select midpoints of Sides AB and CD using Midpoint object snap.
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68. Construct a Line Tangent to a Circle or Arc
Align 45 triangle and straightedge with center of circle and point of tangency (Point P).
Slide triangle until other edge contacts Point P.
Draw line.
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69. Construct a Line Tangent to a Circle or Arc
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70. Construct a Circle or Arc Tangent to a Line at a Given Point
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71. Construct a Circle or Arc Tangent to a Line at a Given Point
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72. Construct a Circle or Arc Through a Point and Tangent to a Line
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73. Construct a Circle or Arc Through a Point and Tangent to a Line
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74. Construct a Circle or Arc Through a Point and Tangent to a Circle
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75. Construct a Circle or Arc Through a Point and Tangent to a Circle
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76. Construct a Circle or Arc Tangent to Two Circles
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77. Construct a Circle or Arc Tangent to Two Circles
Enter Circle command and enter Tangent, Tangent, Radius option.
Pick near one circle to specify first tangent point.
Pick near second circle to specify second tangent point.
Enter given radius.
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78. Construct a Circle or Arc Tangent to a Line and a Circle
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79. Construct a Circle or Arc Tangent to a Line and a Circle
Enter Circle command and Tangent, Tangent, Radius option.
Pick near line to specify first tangent point.
Pick near circle to specify second tangent point.
Enter given radius.
Use Trim command to create arc segments.
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80. Construct a Circle or Arc Tangent to Two Parallel Lines
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81. Construct an Arc Tangent to Two Parallel Lines
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82. Construct a Circle or Arc Tangent to Nonparallel Lines
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83. Construct an Arc Tangent to Nonparallel Lines
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84. Connect Parallel Lines with Reversing Arcs of Equal Radii
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85. Connect Parallel Lines with Reversing Arcs of Equal Radii
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86. Connect Parallel Lines with Arcs of Unequal Radii
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87. Connect Parallel Lines with Arcs of Unequal Radii
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88. Lay off the Length of the Circumference of a Circle
Draw Line AB equal to three times circle diameter.
Strike Arc C equal to circle radius.
Draw Line DE perpendicular to centerline.
Line EB is rectified length.
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89. Calculate and Lay off the Circumference of a Circle
Multiply circle diameter by pi ().
Lay off length on straight line.
For CAD applications, enter List command and pick circle to display value.
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90. Lay off the Length of an Arc
Draw Chord AB. Draw Line CA equal to one-half Line AB.
Draw Line AD.
Draw Arc BD with radius equal to Line BC.
Line AD is arc length.
Use List command in CAD to obtain length.
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91. Lay off a Given Length on an Arc
Divide tangent line of specific length (Line AB) into four parts.
Strike Arc DB from Point C with radius of CB.
Arc AD is equal in length to Line AB.
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92. Lay off a Given Length on an Arc
Divide tangent line of specific length (Line AB) into four parts.
Draw circle from Point C with radius of CB.
Arc AD is equal in length to Line AB.
Use Arc command for arc segments if chord length is known.
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93. Review Questions 1. Which of the following is used to bisect a line?
A. Dividers
B. Scale
C. Template
D. Compass
D. Compass
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94. Review Questions
2. Which of the following is used to draw a line through a point parallel to a given line?
A. Dividers
B. Scale
C. Triangle and T-square
D. Protractor
C. Triangle and T-square
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95. Review Questions The _____ command can be used to draw parallel lines.
A. Spline
B. Offset
C. Divide
D. Arc
B. Offset
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96. Review Questions
4. The _____ method is used to divide a line into equal parts.
A. vertical line
B. construction
C. compass
D. 3,4,5
A. vertical line
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97. Review Questions 5. A(n) _____ angle is an angle more than 90. obtuse
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98. Review Questions
6. Which of the following is used to measure and lay out angles?
A. Dividers
B. Scale
C. Protractor
D. Template
C. Protractor
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99. Review Questions
7. A(n) _____ triangle has all sides and all angles equal.
equilateral
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100. Review Questions 8. The _____ command is used to transfer an angle.
Rotate
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101. Review Questions hexagon
9. A(n) _____ is a regular polygon with six equal sides.
hexagon
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102. Review Questions
10. Which of the following is not specified when drawing objects with the Polygon command?
A. Number of sides
B. Major axis
C. Center point
D. Side length
B. Major axis
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103. Review Questions
11. When using the Polygon command to construct an octagon, use the _____ option if the distance across the corners is known.
Inscribed
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104. Review Questions
12. A(n) _____ is a line or curve that touches the surface of a circle or an arc at only one point.
tangent
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105. Review Questions
13. Which of the following options is not used when drawing circles with the Circle command?
A. Three Points
B. Two Points
C. Tangent, Tangent, Radius
D. Edge
D. Edge
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106. Review Questions
14. Laying off the circumference of a circle is also referred to as locating the _____ length.
rectified
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107. Review Questions
15. The _____ length is the length of a line that connects the endpoints of an arc.
chord
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108. Glossary Arc Bisect Chord length A part of a circle.
To divide something into two equal parts.
Chord length
The length of a line that connects the endpoints of an arc.
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109. Glossary Diameter Equilateral triangle
The length of a straight line passing through the center of a circle and terminating at the circumference on each end.
Equilateral triangle
A triangle with three equal sides and three equal angles (three 60° angles).
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110. Glossary Hexagon Hypotenuse Isosceles triangle
A polygon having six sides.
Hypotenuse
The side directly opposite the 90° angle of a right triangle.
Isosceles triangle
A triangle with two equal sides and two equal angles.
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111. Glossary Octagon Pentagon Perpendicular A polygon having eight sides.
A polygon having five sides.
Perpendicular
A line or plane drawn at a right angle (90 angle) to a given line or plane.
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112. Glossary Polar coordinates Polygon Radius
Point locations measured by entering a given distance and angle from a previous point.
Polygon
A plane geometric figure with three or more sides.
Radius
The straight-line distance from the center of a circle or arc to its circumference.
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113. Glossary Rectified length Regular polygon
The length of a curved surface laid out on a straight line.
Regular polygon
An object with sides of equal length and included angles.
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114. Glossary Right triangle Tangent A triangle with one 90 angle.
A line or curve drawn to the surface of an arc or circle so that it contacts the arc or circle at only one point. A line drawn from the center of the circle or arc to the point of tangency is perpendicular to the tangent object.
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