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Front, Side and Top View with Angles

Front, Side and Top View with Angles
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2014-05-21 20:25
AngleCoordinate GeometrySolid Geometry
In collections Cuboids & their Nets
This example demonstrates the relationship between the front, side, and top views and angles. Key mathematical concepts include similar triangles and angles. Using GeoGebra commands such as Circle, Point, Angle, Segment, Vector, and Polygon, the front, side, and top views are constructed. Suitable for students in middle school and above to learn solid geometry and angle relationships.

GeoGebra Commands & Parameters

  1. Circle(rotateUDc, rotateUD0) → d
  2. Point(d) → rotateUD
  3. Angle(rotateUD0, rotateUDc, rotateUD) → β
  4. Circle(rotateLRc, rotateLR0) → c
  5. Point(c) → rotateLR
  6. Angle(rotateLR0, rotateLRc, rotateLR) → α
  7. Segment(rotateLRc, rotateLR0) → a
  8. Segment(rotateLRc, rotateLR) → b
  9. Segment(rotateUDc, rotateUD0) → e
  10. Segment(rotateUDc, rotateUD) → f
  11. Vector(O, O + (0.0, sin(β + δ * front - β * top))) → Oz
  12. Vector(O, O + (-1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * sin(α + γ * front + γ * top), cos(α + γ * front + γ * top) * cos(β + δ * front - β * top))) → Oy
  13. Vector(O, O + (cos(α + γ * front + γ * top), sin(α + γ * front + γ * top) * cos(β + δ * front - β * top))) → Ox
  14. Polygon(A8, A6, A5, A7) → poly1, a8, a6, a5, a7
  15. Polygon(A6, A4, A3, A5) → poly2, a6_1, a4, a3, a5_1
  16. Polygon(A4, A1, A2, A3) → poly3, a4_1, a1, a2, a3_1
  17. Polygon(A5, A7, A9, A3) → poly4, a5_2, a7_1, a9, a3_2
  18. Polygon(A3, A2, A10, A13) → poly5, a3_3, a2_1, a10, a13
  19. Polygon(A13, A10, A11, A12) → poly6, a13_1, a10_1, a11, a12
  20. Polygon(A9, A3, A13, A12) → poly7, a9_1, a3_4, a13_2, a12_1
  21. Vector(O_2, O_2 + (cos(α + γ * front + γ * top), sin(α + γ * front + γ * top) * cos(β + δ * front - β * top))) → O_2x
  22. Vector(O_2, O_2 + (-1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * sin(α + γ * front + γ * top), cos(α + γ * front + γ * top) * cos(β + δ * front - β * top))) → O_2y
  23. Vector(O_2, O_2 + (0.0, sin(β + δ * front - β * top))) → O_2z
  24. Vector(O_3, O_3 + (cos(α + γ * front + γ * top), sin(α + γ * front + γ * top) * cos(β + δ * front - β * top))) → O_3x
  25. Vector(O_3, O_3 + (-1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * sin(α + γ * front + γ * top), cos(α + γ * front + γ * top) * cos(β + δ * front - β * top))) → O_3y
  26. Vector(O_3, O_3 + (0.0, sin(β + δ * front - β * top))) → O_3z
  27. Polygon(A15, A16, A17, A18) → poly8, a15, a16, a17, a18
  28. Polygon(A16, A22, A25, A17) → poly9, a16_1, a22, a25, a17_1
  29. Polygon(A25, A22, A23, A24) → poly10, a25_1, a22_1, a23, a24
  30. Polygon(A17, A21, A19) → poly11, h, i, j
  31. Polygon(A17, A25, A24, A21) → poly12, a17_2, a25_2, a24_1, a21
  32. Polygon(A19, A20, A18, A17) → poly13, a19, a20, a18_1, a17_3
  33. Polygon(A30, A27, A28, A29) → poly14, a30, a27, a28, a29
  34. Polygon(A36, A34, A35) → poly15, a35, a36, a34
  35. Polygon(A29, A33, A28) → poly16, k, l, m
  36. Polygon(A31, A29, A33) → poly17, n, p, q
  37. Polygon(A31, A32, A30, A29) → poly18, a31, a32, a30_1, a29_1
  38. Polygon(A33, A36, A34, A28) → poly19, r, s, t, a_1
  39. Polygon(A20, A18, A17, A19) → poly20, a20_1, a18_2, a17_4, a19_1
  40. Polygon(A32, A30, A29, A31) → poly21, a32_1, a30_2, a29_2, a31_1
  41. Polygon(A33, A28, A34, A36) → poly22, b_1, c_1, d_1, e_1

AI Drawing Prompt Reference

Draw a 3D object with its three views: front, side, and top. Start by drawing the boundary lines for each view, then add angle markings. Construct similar triangles using angle and segment relationships to determine the positions of vertices. Finally, connect the vertices to form polygons, showing the structure of the 3D object.
The prompt above was compiled from the original drawing commands and is for reference only.