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Properties of a Rhombus by Tan Chee Kian (2)

Properties of a Rhombus by Tan Chee Kian (2)
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2015-05-27 12:43
PolygonAngleCoordinate Geometry
This example demonstrates the properties of a rhombus. Key mathematical concepts include the definition of a rhombus, properties of diagonals, and area calculation. It is constructed using GeoGebra commands such as Circle, Point, Intersect, etc. Suitable for middle school and above students to learn geometric construction.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c_1
  2. Circle(B, A) → d_1
  3. Point(d_1) → C
  4. Circle(C, B) → e_1
  5. Intersect(c_1, e_1, 2) → D
  6. Segment(A, D) → AD
  7. Segment(D, C) → CD
  8. Segment(B, C) → BC
  9. Segment(A, B) → AB
  10. Segment(A, C) → AC
  11. Segment(B, D) → BD
  12. Intersect(AC, BD) → E
  13. Angle(D, E, C) → CED
  14. Angle(D, E, A) → AED
  15. Angle(A, E, B) → AEB
  16. Angle(B, E, C) → BEC
  17. Angle(A, D, C) → ADC
  18. Angle(D, A, B) → BAD
  19. Angle(A, B, C) → ABC
  20. Angle(B, C, D) → BCD
  21. Angle(B, A, E) → BAE
  22. Angle(D, A, E) → DAE

AI Drawing Prompt Reference

Draw a rhombus. The rhombus consists of four points A, B, C, and D, where A and B are adjacent vertices, B and C are adjacent, C and D are adjacent, and D and A are adjacent. The diagonals AC and BD intersect at point E. The four angles of the rhombus are angle ABC, angle BCD, angle CDA, and angle DAB. The diagonals divide the rhombus into four congruent triangles. The construction order is to draw points A and B first, then points C and D, then draw diagonals AC and BD, and finally mark the intersection point E.
The prompt above was compiled from the original drawing commands and is for reference only.