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Muhammad Mustafa's Geometric Construction

Muhammad Mustafa's Geometric Construction
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2020-01-21 14:45
TriangleSolid GeometryGeometric Construction
This example demonstrates the geometric construction of a tetrahedron. It involves key mathematical concepts such as tetrahedron, midpoint, circle, and segments. Using GeoGebra commands like Point, Tetrahedron, Polygon, Centroid, etc., the various faces and edges of the tetrahedron can be constructed. Suitable for high school geometry education and teaching.

GeoGebra Commands & Parameters

  1. Point(Circle[Midpoint[A, B], (Distance[A, B] * sqrt(3) / 2), Segment[A, B]]) → C
  2. Tetrahedron(A, B, C) → a, D, edgeCD, edgeBD, faceABC, faceACD, faceABD, faceBCD, edgeAC, edgeAB, edgeBC, edgeAD
  3. Polygon(D, A, B) → t1, b, d, a_1
  4. Polygon(C, D, A) → t2, a_2, c, d_1
  5. Centroid(t1) → E
  6. Centroid(t2) → F
  7. Midpoint(D, A) → G
  8. Midpoint(D, B) → H
  9. Midpoint(A, B) → I
  10. Circle(G, H, I) → e
  11. Midpoint(D, C) → J
  12. Midpoint(C, A) → K
  13. Circle(J, G, K) → f
  14. Line(J, F) → g
  15. Point(f) → L
  16. Point(e) → M
  17. Line(L, F) → h
  18. Intersect(h, f, 1) → N
  19. Segment(L, N) → i
  20. Line(M, E) → j
  21. Intersect(j, e, 1) → O
  22. Segment(M, O) → k
  23. PointIn(t1) → Pointt1_1
  24. PointIn(t1) → Pointt1_2
  25. PointIn(t1) → Pointt1_3
  26. PointIn(t1) → Pointt1_4
  27. PointIn(t1) → Pointt1
  28. Polygon(C, D, B) → t3, b_1, c_1, d_2
  29. Centroid(t3) → P
  30. Polygon(C, A, B) → t4, b_2, c_2, a_3
  31. Centroid(t4) → Q
  32. Midpoint(C, B) → R
  33. Circle(K, I, R) → s
  34. Circle(H, J, R) → t
  35. Point(t) → S
  36. Point(s) → T
  37. Line(S, P) → l
  38. Intersect(l, t, 1) → U_1
  39. Segment(S, U_1) → m
  40. Point(s) → V
  41. Line(V, Q) → n
  42. Intersect(n, s, 1) → W
  43. Segment(W, V) → p
  44. Segment(S, Z) → q
  45. Segment(U_1, Z) → r
  46. Segment(V, Z) → f_1
  47. Segment(W, Z) → g_1
  48. Segment(M, Z) → h_1
  49. Segment(O, Z) → i_1
  50. Segment(L, Z) → j_1
  51. Segment(N, Z) → k_1