Mastering Geometric Constructions: Drafting Techniques & Skills

2. Chapter 6 Basic Geometric Constructions Section 2Drafting 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.

4. Objectives • Draw triangles, squares, hexagons, and octagons. • Use special techniques to construct regular polygons. • Construct circles and arcs.

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.

6. Constructions for Straight Lines • Bisecting lines • Drawing parallel lines • Drawing perpendicular lines • Dividing lines

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.

8. Bisect a Line • Enter Line command and enter Midpoint object snap. • Pick near midpoint of Line AB. • Draw line in any direction.

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.

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.

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.

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.

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.

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.

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.

16. Constructions for Angles • Bisecting angles • Transferring angles • Drawing perpendiculars • Laying out angles

17. Angle Symbols and Types of Angles

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.

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.

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.

21. Transfer an Angle

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.

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.

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.

25. Lay Out a Given Angle • Enter Line command and use polar coordinatesto draw inclined line at 60. • Specify Point C as first point. • Enter @6<60 as second point. • Polar tracking and direct distance entry allow for specific distance.

26. Polygon and Regular PolygonTypes

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.

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.

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.

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.

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.

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.

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.

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.

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.

36. Construct a Right Triangle • If lengths of two sides forming 90 angle are known, construct perpendicular. • Join ends to form hypotenuse.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

47. Construct a Hexagonwith Distance across Flats Given • Draw circle equal in diameter to given distance. • Draw lines tangent to circle. • Draw remaining sides.

48. Construct a Hexagonwith 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.

49. Construct a Hexagonwith Distance across Corners Given • Draw circle equal in diameter to given distance. • Draw 60 lines across center. • Join intersection points.

50. Construct a Hexagonwith 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.