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Adjacent Angles of a Parallelogram

Adjacent Angles of a Parallelogram
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2017-10-13 17:00
PolygonAngleTransformation
In collections Quadrilaterals الرُباعيات
This example illustrates the properties of adjacent angles in a parallelogram. Adjacent angles are the two angles that are next to each other in a parallelogram and add up to 180 degrees. Using GeoGebra commands such as Polygon, Angle, Intersect, etc., it dynamically shows the characteristics of these angles. Suitable for middle and high school students learning geometry and trigonometry.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → poly1, a, b, c, d
  2. Angle(C, D, A) → α
  3. Intersect(Segment[A, C], Segment[B, D]) → O
  4. Rotate(C, 180°, O) → C1
  5. Rotate(D, 180°, O) → D1
  6. Rotate(A, 180°, O) → A1
  7. Angle(C1, D1, A1) → β
  8. Angle(D, A, B) → γ
  9. Rotate(D, 180°, O) → D2
  10. Rotate(A, 180°, O) → A2
  11. Rotate(B, 180°, O) → B2
  12. Angle(D2, A2, B2) → δ
  13. Vector(D, A) → u
  14. Translate(C, Vector[(e * u)]) → C3
  15. Translate(A, Vector[(e * u)]) → A3
  16. Translate(B, Vector[(e * u)]) → B3
  17. Translate(D, Vector[(e * u)]) → D3
  18. Angle(C3, D3, A3) → ε
  19. Angle(B3, C3, D3) → ζ
  20. Line(D, A) → f
  21. Line(C, B) → g
  22. Vector(C, D) → v
  23. Translate(A, Vector[(h * v)]) → A4
  24. Translate(B, Vector[(h * v)]) → B4
  25. Translate(C, Vector[(h * v)]) → C4
  26. Translate(D, Vector[(h * v)]) → D4
  27. Angle(A4, B4, C4) → η
  28. Angle(B4, C4, D4) → θ
  29. Line(A, B) → i
  30. Line(C, D) → j

AI Drawing Prompt Reference

Draw a parallelogram ABCD, then mark the adjacent angles. First, draw the parallelogram, then label angles A and D, and find the intersection point O of the diagonals. Next, draw angles C1 and D1, which are angles C and D rotated 180 degrees around point O. Then, draw angles A1 and B1, which are angles A and B rotated 180 degrees around point O. After that, draw vector u and translate points C, A, B, and D along vector u to get new points C3, A3, B3, and D3, then draw angle C3D3A3 and angle B3C3D3. Finally, draw vector v and translate points A, B, C, and D along vector v to get new points A4, B4, C4, and D4, then draw angle A4B4C4 and angle B4C4D4.
The prompt above was compiled from the original drawing commands and is for reference only.