1. Design and Communication Graphics
The Oblique Plane

2. Oblique Planes 1
Pictorial views of three planes are shown. In the space provided below draw the line of intersection of these planes with the planes of reference (traces of the planes).

3. Oblique Planes 1
At the end of this sheet, the students should be able to
Draw the line of intersection between the various planes and the planes
of reference
Understand what is meant by the vertical and horizontal trace of simply inclined planes. (resource DVD, Plane and descriptive geometry slides No )
Realise that the inclination of the inclined plane to the vertical plane is seen in plan
The inclination of the inclined plane to the horizontal plane is seen in elevation

4. Oblique Planes 1

5. Oblique Planes 2

6. Oblique Planes 2
At the end of the sheet the students should be able to
Determine the projections of solids cut by simply inclined planes
Determine the true shape of sections cut by simply inclined planes
Understand the concept of rebating planes ( see Resource DVD Plane and Descriptive geometry slide No )

7. Oblique Planes 2

8. Oblique Planes 3 A pyramid is cut by a simply inclined plane as shown.
Complete the elevation and show the true shape of the cut section
A cone cut by a simply inclined plane is used to design the seat shown.
Complete the plan and show the true shape of the cut section

9. Oblique Planes 3
At the end of this sheet , the students should be able to
Determine the projections of objects cut by simply inclined planes
Determine the true shape of the cut sections
Practice rebatting inclined planes

10. Oblique Planes 3

11. Oblique Planes 4

12. Oblique Planes 4
At the end of this sheet, the students should be able to
Distinguish between simply inclined and obliquely inclined plane surfaces
Understand the concept of a plane surface defined by its traces
Draw the projections of lines on an oblique plane that are parallel to the HP
Draw the projections of lines on an oblique plane that are parallel to the VP

13. Oblique Planes 4

14. Oblique Planes 5
The building shown consists of a cylinder cut by an oblique plane.
The incomplete elevation and plan of the cylinder and the traces of
an oblique plane are shown below.
(a) Complete the elevation and determine the true shape of the cut surface.
(b) Identify the major and minor axes in the true shape of the cut surface.
Copenhagen Planetarium

15. Oblique Planes 5
At the end of this sheet the students should be able to
Draw an edge view of an oblique plane (convert an oblique plane into a simply inclined plane)
Determine the projection of solids cut by an oblique plane
Rebatt an oblique plane
Establish the true shape of objects cut by an oblique plane

16. Oblique Planes 5

17. Oblique Planes 6

18. Oblique Planes 6
At the end of this sheet the students should be able to
Locate points on the oblique plane in elevation from the plan.
See also Resource DVD, Plane and Descriptive geometry slides No
Show by two methods the inclination of the oblique plane to the horizontal plane
Establish the true shape of the cut section

19. Oblique Planes 6

20. Oblique Planes 7

21. Oblique Planes 7
At the end of this sheet, the students should be able to
Draw cut sections of a sphere knowing that a sphere cut by any plane will produce circular sections
Locate points in elevation from the plan

22. Oblique Planes 7

23. Oblique Planes 8
The partial elevation and plan of a jewellery display stand is shown.
Draw the projections of the jewellery stand when cut by the oblique plane VTH.

24. Oblique Planes 8
At the end of this sheet the students should be able to
Apply what they have learnt from the previous sheets to solve the problem

25. Oblique Planes 8

26. Oblique Planes 9

27. Oblique Planes 9
At the end of this sheet the students should be able to
Understand that any point on the plane touching the XY line in elevation is on the Horizontal Trace in plan
Understand that any horizontal line on the plane in elevation, will be parallel to the horizontal trace in plan

28. Oblique Planes 9

29. Oblique Planes 10

30. Oblique Planes 10
At the end of this sheet, the students should be able to
Draw the traces of an oblique plane given its inclination to the horizontal plane by two methods.
Find the inclination of the oblique plane to the vertical plane.

31. Oblique Planes 10

32. Oblique Planes 11

33. Oblique Planes 11
At the end of this sheet, the students should be able to
Use information gathered in the previous sheet to complete the elevation and plan of the cut solid
Establish the true shape of the cut section
Establish that the true length of the handle will be seen in the auxiliary elevation
Understand that the right angle will be seen if one line is seen as a true length
Understand that a line perpendicular to a plane is perpendicular to every line on that plane

34. Oblique Planes 11

35. Oblique Planes 12

36. Oblique Planes 12
At the end of this sheet, the students should be able to
Identify the dihedral angle between two intersecting vertical surfaces
Determine the dihedral angle between two intersecting roof surfaces when given the line of intersection which is horizontal
Determine the dihedral angle between two intersecting planes
Determine the line of intersection between two intersecting planes

37. Oblique Planes 12

38. Oblique Planes 13

39. Oblique Planes 13
At the end of this sheet, the students should be able to
Determine the traces of oblique planes that contain given surfaces
Determine the line of intersection between two planes
Determine the inclination of a plane to the planes of reference

40. Oblique Planes 13

41. Oblique Planes 14

42. Oblique Planes 14
At the end of this sheet, the students should be able to
Determine the horizontal and vertical traces of two intersecting laminae
Determine the line of intersection between oblique planes from their traces
Determine the dihedral angle between two oblique planes from their traces
Determine the angle of inclination of an oblique plane to the planes of reference

43. Oblique Planes 14

44. Oblique Planes 15

45. Oblique Planes 15
At the end of this sheet, the students should be able to
Determine the height and draw the elevation of the roof surfaces A, B and C
Determine the true length of an oblique line
Establish the dihedral angle between two intersecting roof surfaces
Establish the true shape of an obliquely inclined plane
Determine the projections of a line drawn from point X which is 45mm long and rests on the roof surface C
Determine the true inclination of a line to the H.P.

46. Oblique Planes 15

47. Oblique Planes 16

48. Oblique Planes 16
At the end of this sheet, the students should be able to
Determine the true length of the line of intersection between two planes
Determine the dihedral angle between two planes
Determine the true shape of oblique planes
Determine the projections of a line 45mm long resting on a plane having an apparent angle of 45 degrees
Solve problems involving the reversal of the dihedral angle between two planes

49. Oblique Planes 16