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The Main Menu

M 2. h 2. v 2 = v. Locus of M 2. 3 cm. v 1. x 12. 2 cm. h 1. Locus of M 1. M 1. Next. The Main Menu. ا Previous. Example (3). Given a plane (5,3,4). Represent M (?, 2, 3). o. R. M 2. m 2. C. M. x 12. B. D. A. m 1. m. Next. The Main Menu. ا Previous. Example (4).

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The Main Menu

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  1. M2 h2 v2 = v Locus of M2 3 cm v1 x12 2 cm h1 Locus of M1 M1 Next The Main Menu اPrevious Example (3) Given a plane (5,3,4). Represent M (?, 2, 3). o

  2. R M2 m2 C M x12 B D A m1 m Next The Main Menu اPrevious Example (4) Given a point M2 and the two projections of a str. Line m. Represent a regular tetragonal pyramid ABCDR whose base is a square ABCD , its edge RA and its edge RB passes thr. M. .

  3. EXAMPLE 4 • Represent a regular tetragonal pyramid ABCDR if its base ABCD lies in H.P.,its edge AR lies on a given straight line m and the vertical projection of a point M lying on the edge BR is given R m M m M D x C m B A

  4. R m M N A x A D C B C A R m N M B

  5. R2 L2 M2 m2 C2 B2 A2 D2 x12 D1 C1 P1 N1 L1 m1 M1 A1 B1 Next The Main Menu اPrevious R1

  6. M2 m1 x12 m2 M1 Next The Main Menu اPrevious Example (5) Represent a cone of revolution if its base is a circle . A generator of the cone lies on the given str. Line m. The given point M lies on the surface of the cone. R . M A s m

  7. EXAMPLE 5 • Represent a cone of revolution if its base circle is in H.P. A generator of the cone lies on the given straight line m. the given point M lies on the surface of the cone . . m M M x m m m M

  8. R2 N2 m2 A2 S2 x12 . S1 . // // m1 N1 A1 Next The Main Menu اPrevious M2 R1 M1

  9. Aux. Aux. // تحويل المستوى لخط Aux. m Aux. // m لإيجاد الشكل الحقيقىT. S لإيجاد مستوى // مستوى ويبعد عنه مسافة تحويل المستقيم لنقطة T. L of m ايجاد أقصر مسافة بين خطين متخالفين ايجاد الزاوية الزوجية بين شكلين Next The Main Menu اPrevious ORTHOGONAL AUXILIARY PROJECTION

  10. Next The Main Menu اPrevious ORTHOGONAL AUXILIARY PROJECTION Definition: The auxiliary projection planes are used in the case of transformations of positions of geometric objects into more simple positions, from which the properties of the objects are found. In these new positions the complex problems can be solved easily. The side projection plane can be considered as an auxiliary projection plane

  11. A v A A A A A A A h A A The auxiliary projection plane is a vertical plane The auxiliary projection plane is normal to V.P.

  12. M2 // x12 M4 // M1 M2 // x24 x13 M3 // x12 M1 Next The Main Menu اPrevious The auxiliary projection plane is The auxiliary projection plane is

  13. x24 M2 M4 // M2 x12 M1 // x12 M1 Next The Main Menu اPrevious Successive orthogonal projection on auxiliary projection planes: M6 } // x46 * } } * * // M3 x13 } * M5 x35

  14. A6 = B6 x46 } B2 // A2 B4 x12 A1 T. L // } A4 A3 B1 B2 } x24 A2 T. L // x13 x12 B3 x35 . A3 // } A5 = B5 B1 Next The Main Menu اPrevious The orthogonal projection of a straight line on an auxiliary projection planes: m2 m1 m2 m1

  15. A2 // A1 x12 x12 A4 x13 // // . A3 . x24 A2 // A1 Next The Main Menu اPrevious The orthogonal projection of a a plane on an auxiliary projection planes: B1 = B2 B4 B3 B1 = B2

  16. V2 L2 M2 N2 x13 x12 M1 L1 N1 V3 N3 M3 L3 x35 N5 L5 T. S M5 Next The Main Menu اPrevious Successive orthogonal projection of a a plane on an auxiliary projection planes:

  17. C2 D2 A2 B2 x12 C1 A1 B1 D1 Next The Main Menu اPrevious Example (1) Given the two triangles ABC and ABD, by their horizontal and vertical projections. AB is a horizontal straight line. Find the dihedral angle between the two planes of the triangles.

  18. / * // // C2 x23 D2 * A2 B2 . // x12 C1 A1 / B1 D1 Next The Main Menu اPrevious T. L C3 A3 =B3 D3

  19. B2\ C2\ D2\ A2\ C2 B2 D2 A2 x12 D1 = D1\ C1 = C1\ A1 = A1\ B1 = B1\ Next The Main Menu اPrevious Example (2) A cube ABCDD\C\B\A\ rests on by its face ABCD. Find the projections of the cube on two auxiliary projection planes and .

  20. A\4 B\4 B4 A4 C\4 D\4 x24 C4 D4 C3 D3 B3 A3 C\3 x13 D\3 B\3 Next A\3 The Main Menu اPrevious C\2 B\2 D\2 A\2 C2 B2 D2 A2 x12 D1 = D1\ C1 = C1\ A1 = A1\ B1 = B1\

  21. A2 m2 M2 B2 x12 M1 B1 m1 A1 Next The Main Menu اPrevious Example (3) Given a point M and a straight line m:{A, B} where . Find d(M, m). i.e the distance of the point M from the straight line m.

  22. * // // / / A2 m2 M2 B2 /// /// ** x12 B3 * M1 T.L B1 m3 m1 x13 A1 M3 A3 ** /// A5 = m5 =B5 d (M, m) M5 x35

  23. // x12 x13 // 2 cm Next The Main Menu اPrevious Example (4) Given a plane by its two traces and and it is required to construct the traces of a plane and at a distance 2 cm from .

  24. M2 C2 A2 B2 x12 B1 C1 A1 Next The Main Menu اPrevious Example (5) Given ABC by its two projections and the vertical projection M2 of the point M. Find M1 if d( M, ABC ) = 2.5 cm.

  25. M2 C2 /// /// // // A2 * * B2 / / B1 . M1 C1 B3 A1 . M3 A3 2 .5 cm Locus of M C3 x13 Next The Main Menu اPrevious x12

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