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OLEH PN. CHUANG BEE ENG SM TEKNIK BATU PAHAT

LINES AND PLANES IN THREE DIMENSIONS. OLEH PN. CHUANG BEE ENG SM TEKNIK BATU PAHAT. ACTIVITY 1 : TO IDENTIFY THE PLANE . G. H. E. F. D. C. A. B. PLANE AT THE TOP :. PLANE EFGH. G. H. E. F. D. C. A. B. PLANE ON THE LEFT :. PLANE ADHE. G. H. E. F. D. C. A. B.

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OLEH PN. CHUANG BEE ENG SM TEKNIK BATU PAHAT

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  1. LINES AND PLANES IN THREE DIMENSIONS OLEH PN. CHUANG BEE ENG SM TEKNIK BATU PAHAT

  2. ACTIVITY 1 : TO IDENTIFY THE PLANE G H E F D C A B PLANE AT THE TOP : PLANE EFGH

  3. G H E F D C A B PLANE ON THE LEFT : PLANE ADHE

  4. G H E F D C A B PLANE IN THE FRONT : PLANE ABFE

  5. G H E F D C A B PLANE AT THE BACK : PLANE DCGH

  6. G H E F D C A B PLANE AT THE BOTTOM: PLANE ABCD

  7. G H E F D C A B PLANE ON THE RIGHT : PLANE BCGF

  8. THE LOCATION OF THE POINT ON TOP OF THE RED DOT TO THE RIGHT OF THE RED DOT AT THE BACK OF THE RED DOT IN FRONT OF THE RED DOT

  9. ON THE TOP OF …. AT THE BACKOF …. TO THE LEFT OF …. TO THE RIGHT OF …. IN FRONT OF …. AT THE BOTTOMOF ….

  10. H G E F D C A B ACTIVITY 2 : TO DETERMINE THE LOCATION OF A POINT POINT E POINT TO THELEFTOF F : POINT AT THE BOTTOM OF F : POINT B POINT AT THE BACK OF F : POINT G POINT TO THE RIGHT OF D : POINT C POINT ON TOP OF D : POINT H POINT IN FRONT OF D : POINT A

  11. ANGLE BETWEEN A LINE AND A PLANE A LINE PLANE B C

  12. Activity 3 :To Identify The Angle Between Line And Plane H G The line draw from G and perpendicular to the plane ABCD is call normal Normal E F D C The line lies on the plane ABCD which joint the point A to the line GC is known as the orthogonal projection of line AG on the plane ABCD. Orthogonal projection A B The angle between the line AG and the orthogonal projection, AC is the angle between the line AG and the plane ABCD that is GAC.

  13. ACTIVITY 3 : To Identify The Angle Between A Line And A Plane Example 1a H G C A G Normal E F D At the bottom C Name the angle between the line AG and the plane ABCD A B Orthogonal projection Angle between the line AG and the plane ABCD = GAC.

  14. H G E F D C A B Diagram 1(b) EXAMPLE 1(b) Diagram 1b shows a cuboid ABCDEFGH. Name the angle between the line HB and the plane ABCD.

  15. 12cm G H 5cm 5cm E F D C 4cm A B Diagram 2a ACTIVITY 4 : To find the angle between a line and a plane Example 2(a) Diagram 2(a) shows a cuboid, ABCDEFG. Find the angle between the line AH and the plane DCGH.

  16. No Steps Solutions 1. Draw the line AH and shade the plan DCGH in diagram 2a. 12cm H G 5cm E F D C 4cm A B Diagram 2a Diagram 2a shows a cuboid, ABCDEFG. Find the angle between the lineAHand the plane DCGH.

  17. 12cm H G 5cm E F D C 4cm A B A H D back

  18. A H D H A D 12cm H G 5cm E F D C 4cm A B

  19. H 5 cm A D 4 cm 12cm H G 5cm E F D C 4cm A B

  20. 12cm H G 5cm E F D C 4cm A B H Mark, - the opposite side, AD asT - the adjacent side, HD as S 5 cm S A D 4 cm T

  21. 12cm H G 5cm E F D C 4cm A B - SOH – CAH – TOA

  22. example 2 (b) 12 cm H G E F 4 cm D C 3 cm A B Diagram 2b Diagram 2b shows a cuboid,ABCDEFGH. Calculate the angle between the line HB and the plane BCGF

  23. ANGLE BETWEEN TWO PLANES

  24. ACTIVITY 5 : To Identified The Angle Between Two Planes EXAMPLE 3(a) G H E F D C • DRAW 3 LINES A B Diagram 3a Diagram 3a shows a cuboid, ABCDEFGH. Name the angle between the plane AGH and the plane ABCD

  25. ACTIVITY 5 : To Identified The Angle Between Two Planes G H E F D C Bottom A B • Mark the location (direction) of the plane ABCD at the bottom of the first line to the left. Diagram 3a Diagram 3a shows a cuboid, ABCDEFGH. Name the angle between the plane, AGH and the plane, ABCD

  26. ACTIVITY 5 : To Identified The Angle Between Two Planes G H A E F D C Bottom A • Refer to the plane, AGH, identify the points which touch the plane, ABCD and write it at the middle line. B Diagram 3a Diagram 3a shows a cuboid, ABCDEFGH. Name the angle between the plane, AGH and the plane, ABCD

  27. ACTIVITY 5 : To Identified The Angle Between Two Planes G H H / G A E F D Bottom C • Refer to the plane, AGH, identify the point which does not touch the plane, ABCD and write it at the first line to the left. A B Diagram 3a Diagram 3a shows a cuboid, ABCDEFGH. Name the angle between the plane, AGH and the plane, ABCD

  28. ACTIVITY 5 : To Identified The Angle Between Two Planes G H/G H A Bottom E F D C • Between the point H and G, point which is nearer to point A or located on the same plane as point A will be choosen. Point which is not choosen will be earased. A B Diagram 3a Diagram 3a shows a cuboid, ABCDEFGH. Name the angle between the plane, AGH and the plane, ABCD

  29. ACTIVITY 5 : To Identified The Angle Between Two Planes G H H A Ke Bawah E F D C • Between the point H and G, point which is nearer to point A or located on the same plane as point A will be choosen. Point which is not choosen will be earased. A B Diagram 3a Diagram 3a shows a cuboid, ABCDEFGH. Name the angle between the plane, AGH and the plane, ABCD

  30. Bottom ACTIVITY 5 : To Identified The Angle Between Two Planes G H H A D E F D C • Identify the point which is located at the bottom of the point H ( )and write it on the first line to the right. A B Diagram 3a Diagram 3a shows a cuboid, ABCDEFGH. Name the angle between the plane, AGH and the plane, ABCD

  31. H A D ACTIVITY 5 : To Identified The Angle Between Two Planes G H E F D C Bottom • In the diagram 3a, complete the ∆ HAD and mark the HAD A B Diagram 3a Angle between the plane, AGH and the plane, ABCD = HAD

  32. 12cm H G 5cm E F D C 4cm A B Diagram 3b EXAMPLE 3(b) Diagram 3b shows a cuboid with horizontal rectangle base ABCD. Name the angle between the plane ACH and the plane CDHG

  33. THANK YOU

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