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Kite, Rhombus, and Square Relationship

Kite, Rhombus, and Square Relationship
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2017-10-03 20:53
PolygonGeometric Construction
This example demonstrates the relationship between a kite, rhombus, and square through geometric construction and calculates the areas of these quadrilaterals. Using GeoGebra commands such as Line, Segment, and Polygon, the properties and area calculation methods of these shapes are clearly shown. Suitable for students at the junior high school level and above.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Segment(C, D) → b
  3. Polygon(B, D, A, C) → Vieleck1, b_1, d, a_1, c
  4. Segment(A, B) → e
  5. Intersect(b, e) → E
  6. Polygon(A, E, D) → Vieleck2, d_1, a_2, e_1
  7. Polygon(A, E, C) → Vieleck3, c_1, a_3, e_2
  8. Polygon(C, E, B) → Vieleck4, b_2, c_2, e_3
  9. Polygon(E, B, D) → Vieleck5, d_2, e_4, b_3
  10. Midpoint(D, A) → F
  11. Midpoint(A, C) → G
  12. Midpoint(C, B) → H
  13. Midpoint(B, D) → I
  14. Rotate(A, α, F) → A'_1
  15. Rotate(E, α, F) → E'_1
  16. Rotate(D, α, F) → D'_1
  17. Polygon(A'_1, E'_1, D'_1) → Vieleck2', d', a', e'
  18. Rotate(E, α, I) → E'_2
  19. Rotate(B, α, I) → B'_1
  20. Rotate(D, α, I) → D'
  21. Polygon(E'_2, B'_1, D') → Vieleck5', d'_1, e'_1, b'
  22. Rotate(A, α, G) → A'
  23. Rotate(E, α, G) → E'_3
  24. Rotate(C, α, G) → C'_1
  25. Polygon(A', E'_3, C'_1) → Vieleck3', c', a'_1, e'_2
  26. Rotate(C, α, H) → C'
  27. Rotate(E, α, H) → E'
  28. Rotate(B, α, H) → B'
  29. Polygon(C', E', B') → Vieleck4', b'_1, c'_1, e'_3
  30. Angle(D, E, A) → β
  31. Textfield(Text21) → Textfeld1
  32. Textfield(Text23) → Textfeld2
  33. Textfield(Text25) → Textfeld3
  34. Polygon(J, K, L, M) → Vieleck6, j, k, l, m