1. Skew Lines
Topic Integration

2. DESIGN AND COMMUNICATION GRAPHICS
Solutions to problems should be taught with….
“an explanation as to how the construction was derived ”
Draft Guidelines for Teachers (page 14)
Two key concepts of plane and descriptive geometry relating to skew lines are
parallel lines
the parallel plane
Understanding the Why rather than knowing the How

3. PROPERTIES AND PROJECTIONS OF SKEW LINES
“Define the concept of skew lines and their use in solving practical problems” page 17 of syllabus
Clearances between cables, pipes and braces
Shortest connecting tunnel between two mine tunnels
Shortest connection between two oblique sewer lines or pipelines

4. Skew lines are lines which are non-intersecting and non-parallel.
Skew lines are non-coplanar
If you look at a bridge over a river, you are looking at an example of skew lines.

5. An overpass is an excellent example of skew lines
An overpass is an excellent example of skew lines. The roadway represents one line and the pedestrian bridge represents another line. The “lines” do not intersect because they are on different planes.

6. C1 A1 C1 A1 D1 B1 B1 D1 A D C B D C B A Which set of lines is skew?
Intersecting Lines
When two lines intersect, the point of intersection will align in elevation and plan, and any other view.
Skew Lines
Skew lines do not intersect. Their apparent point of intersection will not align in elevation, plan or any other view. C1 D B A C A1 D1 B1 C1 A C D B A1 D1 B1
Find the vertical distance between the two skew lines?

7. THE CONCEPT OF A PARALLEL PLANE

8. PARALLEL LINES REMAIN PARALLEL IN EVERY VIEW
Lines which are parallel in space will appear parallel in all views

9. Parallel Lines

10. PARALLEL LINES REMAIN PARALLEL IN EVERY VIEW
Lines which are parallel in space will appear parallel in all views
except
in the views in which they appear as points or
where one line is behind the other

11. PARALLEL PLANE
If a line is parallel to any line in a plane, it is parallel to the plane

12. C B A D The projections of two skew lines AB and CD are shown.
(a) Find a plane containing the line CD and parallel to the line AB.
(b) Prove that the plane is parallel to the line. C B A D

13. Parallel Plane 1

14. M C A D B C
true length (strike) B A
true length (strike) D M C D B A

15. SHORTEST DISTANCE BETWEEN TWO SKEW LINES

16. What types of applications of skew lines are around us?

17. The directions of two parachute jumpers landing are represented by the skew lines AB and CD.
(a) Determine the shortest distance between the two skew lines.
(b) Determine the projections of this shortest distance. A B C D A1 B1 C1 D1

18. Shortest Distance

19. A2 B2 C2 D2 A B C D A1 B1 C1 D1 A3 B3 C3 D3
datum line

20. SHORTEST HORIZONTAL DISTANCE BETWEEN TWO SKEW LINES

21. The directions of two javelins are represented by the skew lines AB and CD.
Determine the projections of the shortest horizontal distance between the two skew lines. A B C D A1 B1 C1 D1

22. Shortest Horizontal

23. A2 B2 C2 D2 A B C D A1 B1 C1 D1 A3 B3 C3 D3
datum line

24. traces of plane directorH V A B C D A1 B1 C1 D1
Where is the other plane director?
traces of plane director

25. Hyperbolic Paraboloid

26. MINING GEOMETRY

27. headwall
Earth’s surface
footwall

28. Skew boreholes
Line on headwall
Line on footwall