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Properties of Lines and Planes of Solids

Properties of Lines and Planes of Solids. Chapter 4. Contents. Perpendicular Line of a Plane Angle between a Line and a Plane Angles between Two Planes Making a Cuboid (For investigating angles found in a cuboid). Perpendicular Line of a Plane. Perpendicular Line of a Plane. Wooden Stick

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Properties of Lines and Planes of Solids

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  1. Properties of Lines and Planes of Solids Chapter 4

  2. Contents • Perpendicular Line of a Plane • Angle between a Line and a Plane • Angles between Two Planes • Making a Cuboid (For investigating angles found in a cuboid)

  3. Perpendicular Line of a Plane

  4. Perpendicular Line of a Plane Wooden Stick (Perpendicular Line) Blue-Tack

  5. Top View: The stick should coincide with the point O. Stick

  6. The stick is perpendicular to all 3 lines: OA, OB and OC. Right Angle

  7. From a different perspective Right Angle

  8. Again from another perspective Right Angle

  9. Top view

  10. Angle between a Line and a Plane D Projection of OD on plane X (Line directly below stick) Plane X

  11. Top view – OD coincides with OA D

  12. Join AD – AD  plane X D Plane X

  13. DOA = Angle between Line OD and Plane X D Angle between line OD and plane X Plane X

  14. Another explanation Light directly above stick

  15. The light casts a shadow on the ground D Angle between stick and horizontal plane Shadow of stick

  16. Top view

  17. Angle between 2 planes P Q

  18. Fold the black line to form 2 planes wooden stick P Q line of intersection of planes A and B

  19. Angle between Planes A and B P Q PXQ = Angle between planes A and B Both PX and QX are  line of intersection

  20. Another perspective PXQ = Angle between planes A and B

  21. Side view PXQ = Angle between planes A and B

  22. Make a Cuboid - Your turn! 12 cm x 4 8 cm x 8

  23. Build the foundation Paper Blu-Tack

  24. Build the foundation Top view

  25. Then build the first wall

  26. Then the second wall

  27. Finally complete the roof

  28. From another perspective

  29. Top view

  30. Angle between red line and blue rectangle = ? E H F G D C A B

  31. Angle between red line and blue rectangle = ? H E F G F C D B A

  32. Angle between BH and Plane ABCD = HBC E H F G D C A HBC Projection of BH on Plane ABCD = BC B

  33. Angle between line AH and Plane ABCD H E G F C D Projection of AH on Plane ABCD = AC A HAC B

  34. Angle between line AH and Plane ABCD = HAC E H F G C D A B

  35. Side View of HAC H A C

  36. Right Angles with G as Vertex (Type A) E H FGH F HGB G FGB D C A B

  37. Right Angles with G as Vertex (Type B) (Involves a diagonal) E H EGB F G AGH FGC D C A B

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