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DIMENSI 3

DIMENSI 3. THREE DIMENSIONS. Distance and Angle (Jarak dan Sudut). Three dimensions. Distance in plane and space Target : Distance between point to point, point to line and point to plane HES Thank you for save/keep our environment. Clean your desk. steps:.

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DIMENSI 3

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  1. DIMENSI 3 THREE DIMENSIONS Distance and Angle (Jarak dan Sudut)

  2. Three dimensions • Distance in plane and space • Target : Distance between point to point, point to line and point to plane • HES Thank you for save/keep our environment Clean your desk

  3. steps: Explaining the study matter (20 minutes) Discussing of the problem (15 minutes) Each of group send one delegate to follow the competition (20 minutes) Quiz (15 minutes) Announcement of the team winner Closing

  4. DISTANCE The distance between point P to line segment AB is the shortest path where the projection from P to line AB is perpendicular P B PP’ is the distance between P to line AB P’ A PP’ is the distance between P to plane AB P P’

  5. Examples: • In the cube ABCD.EFGH with edge 10 cm, find the distance between point A to line FH G H A’ The distance between A to line FH is AA’ F E See the triangle AA’F AF =FH= plane diagonal D C A’F = …(2) A B …(1) From (1) & (2), we get : (AA’)2 = (AF)2 - (A’F)2 = 200 - 50 (AA’)2 = 150 AA’ =

  6. T The distance between B to line AT is BB’ • In the figure below find the distance between B to line AT 5 cm See the triangle APT B’ C D AP = 2 cm, AT = 5 cm 4 cm A P B TP2 = AT2 – AP2 4 cm = 25 - 4 See the triangle ABT The area ABT1 = By using comparison between two areas of triangle, then: The area ABT2 = BB’ =

  7. The distance between C to plane BDG is CC’ • A cube ABCD.EFGH with edge 6 cm, find the distance between point C to plane BDG OC = (OG)2 = (OC)2 + (CG)2 C’ G H F E O = 18 + 36 = 54 D C See the triangle OCG A B The area OCG1 = By using comparison between two areas of triangle, then : The area OCG2 =

  8. TOURNAMENT : session i • In the cube ABCD.EFGH of edge 4 cm, find the distance from point D to the line CH • A cube ABCD.EFGH with edge 8 cm, find the distance from point D to the line BG • A pyramid T.ABCD with edge of base square 6 cm and TA=TB=TC=TD= 5 cm. Find the distance from point A to point C

  9. Session ii • A cube ABCD.EFGH with edge 6 cm. find the distance from point H to line DF • A pyramid T.ABCD with edge of base square 6 cm. TA=TB=TC=TD= Find the distance from point A to line TC • A cube ABCD.EFGH with edge 12 cm. find the distance from point C to line E

  10. SESSION III • A cube ABCD.EFGH with edge 8 cm. find the distance from point H to line DF • A cube ABCD.EFGH with edge 4 cm. find the distance from point A to middle point CG • A cube ABCD.EFGH with edge 11 cm. find the distance from point D to line CF

  11. Session iv • In the cube ABCD.EFGH of edge 6 cm, find the distance from point C to the line BG • In the cube ABCD.EFGH of edge 12 cm, find the distance from point C to the line AH • In the cube ABCD.EFGH of edge 9 cm, find the distance from point C to the plane BDG

  12. Quiz : 15 minutes • A cube ABCD.EFGH with edge 6 cm. find the distance from point H to line DF • A pyramid T.ABCD with edge of base square 3 cm and TA=TB=TC=TD= 5 cm. Find the distance from point T to line BD • A cube ABCD.EFGH with edge 10 cm. find the distance from point A to plane BDE • A pyramid T.ABCD with edge of base square 5 cm and TA=TB=TC=TD= 6 cm. Find the distance from point T to line CD 4

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