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Diagonals of a Rhombus

Diagonals of a Rhombus
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2019-02-21 06:36
PolygonAngleGeometric Construction
This example demonstrates the properties and relationships of the diagonals in a rhombus. Key math concepts include the symmetry of a rhombus, the diagonals being perpendicular bisectors of each other, and the diagonals dividing the rhombus into four congruent right triangles. Construction involves commands/objects like Point, Segment, Line, OrthogonalLine, Intersect, Angle, Polygon in GeoGebra. Suitable for middle school and above students learning geometric constructions and property exploration.

GeoGebra Commands & Parameters

  1. Point(Circle[A, side]) → B
  2. Segment(A, B) → b
  3. Line(A, B) → c
  4. Point(Circle[A, side]) → D
  5. Segment(A, D) → d
  6. Point(Circle[B, side]) → C
  7. Segment(B, C) → e
  8. Line(D, C) → f
  9. Line(C, c) → g
  10. Segment(D, C) → h
  11. Line(E, F) → i
  12. OrthogonalLine(E, i) → j
  13. OrthogonalLine(F, i) → k
  14. Point(k) → G
  15. OrthogonalLine(G, j) → l
  16. Intersect(j, l) → H
  17. Segment(E, H) → m
  18. Segment(H, G) → n
  19. Segment(G, F) → p
  20. Segment(F, E) → q
  21. Angle(E, F, G) → α
  22. Angle(F, G, H) → β
  23. Angle(G, H, E) → γ
  24. Angle(H, E, F) → δ
  25. Angle(B, C, D) → ε
  26. Angle(C, D, A) → ζ
  27. Angle(D, A, B) → η
  28. Angle(A, B, C) → θ
  29. Polygon(I, J, 4) → poly1, i_1, j_1, r, s, K_1, L_1
  30. Angle(I, L_1, K_1) → ι
  31. Angle(L_1, K_1, J) → κ
  32. Angle(K_1, J, I) → λ
  33. Angle(J, I, L_1) → μ
  34. Intersect(s, r) → L
  35. Intersect(j_1, r) → K
  36. Segment(A, C) → t
  37. Segment(D, B) → a_1
  38. Intersect(t, a_1) → M
  39. Segment(M, B) → b_1
  40. Segment(M, D) → c_1
  41. Segment(M, C) → d_1
  42. Segment(M, A) → e_1
  43. Angle(B, M, C) → ν
  44. Angle(D, M, C) → ξ
  45. Angle(A, M, D) → ο
  46. Angle(B, M, A) → ρ
  47. Angle(M, C, B) → σ
  48. Angle(M, C, D) → τ
  49. Angle(C, D, M) → υ
  50. Angle(M, D, A) → φ
  51. Angle(D, A, M) → χ
  52. Angle(A, B, M) → ψ
  53. Angle(M, A, B) → ω
  54. Angle(M, B, C) → α_1
  55. Segment(M, C) → f_1
  56. Segment(M, D) → g_1
  57. Segment(M, B) → h_1
  58. Segment(A, M) → k_1