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Mastering Geometric Constructions: Drafting Techniques & Skills

Learn to create geometric constructions using manual drafting tools and CAD commands. Explore techniques to draw, bisect, divide lines, angles, triangles, squares, and circles effectively. Understand the importance of proper instruments and methods for accurate constructions in drafting.

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Mastering Geometric Constructions: Drafting Techniques & Skills

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

  2. 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.

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

  4. 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.

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

  6. 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.

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

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

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

  16. Angle Symbols and Types of Angles

  17. 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.

  18. 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.

  19. 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.

  20. Transfer an Angle

  21. 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.

  22. 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.

  23. 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.

  24. 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.

  25. Polygon and Regular PolygonTypes

  26. 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.

  27. 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.

  28. 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.

  29. Construct a Triangle with Two Sides and Included Angle Given • Draw Side B. • Draw Side A using polar coordinates or tracking. • Draw remaining side.

  30. 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.

  31. 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.

  32. 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.

  33. 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.

  34. 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.

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

  36. 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.

  37. 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.

  38. 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.

  39. 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.

  40. 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.

  41. 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.

  42. 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.

  43. Construct a Regular Pentagon with Side Length Given • Enter Polygon command and specify five sides. • Enter Edge option and select endpoint. • Enter side length.

  44. 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.

  45. Construct an Inscribed Pentagon with Radius Given • Enter Polygon command and specify five sides. • Pick center point. • Enter Inscribed option and specify given radius.

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

  47. 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.

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

  49. 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.

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