RUANG DIMENSI TIGA

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Transcript of RUANG DIMENSI TIGA

  • THREE DIMENSIONS

  • Basic Competence : Determine state of distance and angle which related point, line and plane on the space three dimensionsIndicators

    Student able to determine state line with line on space three dimensionsStudent able to determine state line with plane on three dimensions

  • STATE Point, line, and plane ON SPACEstate Point with linestate Point with planestate line with line otherstate line with planeI. DefinitionII. state Point, line, and planePointlineplaneAksioma line and plane

  • A. PointAP(a) Point A(b) Point PDefinitiona Point drawed with use sign dot.name a Point usually use capital letters A, B, C, P, Q, or R

  • B. linegA(a) line g(b) Segment line ABD E F I N I TIONa line define with length of light.part from a line called segment line.name from a line using a little alphabet / name segment can look at picture above. B

  • C. plane(a) plane (b) plane ABCD(c) plane (e) plane KLMN

  • AKSIOMA IPassing through two point can only be drawn one straight line.AB

  • State point with linePoint A located on line gAgPoint B out side with line hBh

  • state Point with planePoint A located on plane APoint B out side with plane B

  • state line with others lineA. line g and h concurrent in point AB. line g and h close up

  • C. line g and h paralelD. line g and h crossedh

  • line perpendiculer with planeA line (g)perpendiculer with a two line (k & l),

    line k and l concurrent

    then line g perpendiculer with plane v

    gklg k, g l,k and l concurrent, so g V

  • line perpendiculer with planegabA line g perpendiculer with plane vthen, line g perpendiculer with all line on plane vg a, g b,

  • EXAMPLEShows that line AE perpendiculer with Plane ABCD.Prove :line AE ADline AE ABAD and AB concurrent, AB & AD on plane ABCDThen, AE Plane ABCD

  • Characterictic on cubeIf one from two line paralel, perpendiculer on a plane then line other perpendiculer with that plane tooIf two line perpendiculer with a plane, then that lines paralelThrough a point out side for line, only can form one plane which perpendiculer which that line.

  • EXAMPLEShows that line AE // line DHProve :line AE ABCDline DH ADline DH CDAd and CD concurrent and located on plane ABCDDH ABCD, AE Plane ABCDDH plane ABCDSo, AE // DH

  • ExercisesKnowing Cube ABCD EFGH, with aksioma or characteristic show thats1. AB ADHE2.AB CG3. AB // GH4. AC DF5. AG BDE6. AG CFE

  • THANKSSEE YOU NEXT TIME

  • D. AKSIOMA line and planeIn geometry an three important aksioma. (Euclides, mathematicians drom Alexandria)AKSIOMA IAKSIOMA IIIAKSIOMA IIEuclides

  • AKSIOMA II

    if a line and a plane have two common Point, then all point on line located on planeAB

  • AKSIOMA III

    Passing through three point can form only one planeACB