MathPlotAI Logo MathPlotAI

Exploring Base & Height in Triangles and Related Parallelograms

Exploring Base & Height in Triangles and Related Parallelograms
Loading the math board and drawing, please wait…
2017-11-16 02:14
TrianglePolygonCoordinate GeometryGeometric ConstructionSlider Animation
This example demonstrates how to explore the base and height relationships between triangles and related parallelograms using GeoGebra. Core mathematical concepts include parallelograms, triangles, centroids, limits, and statistics. Construction highlights involve commands and objects like Polygon, Point, Midpoint, Rotate, OrthogonalLine, Line, Intersect, Segment, and Angle. Suitable for high school mathematics students and teachers for geometric construction and concept understanding.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → t1, c, a, b
  2. Point(c) → M
  3. Point(b) → L
  4. Point(a) → G
  5. Midpoint(c) → E
  6. Midpoint(a) → F
  7. Rotate(A, 180°, E) → A'_1
  8. Rotate(B, 180°, E) → B'_1
  9. Rotate(C, 180°, E) → C'
  10. Polygon(A'_1, B'_1, C') → t1'_1, c'_1, a'_1, b'_1
  11. Rotate(A, 180°, F) → A'
  12. Rotate(B, 180°, F) → B'_2
  13. Rotate(C, 180°, F) → C'_2
  14. Polygon(A', B'_2, C'_2) → t1'_2, c'_2, a'_2, b'_2
  15. OrthogonalLine(M, c) → h
  16. Line(A', B) → l
  17. Line(C', A) → m
  18. OrthogonalLine(L, b) → i
  19. Intersect(i, l) → I
  20. OrthogonalLine(G, a) → f
  21. Intersect(f, a) → J
  22. Intersect(f, m) → K
  23. Segment(K, G) → height_2
  24. Segment(L, I) → height_3
  25. Segment(A, C) → base_3
  26. Segment(A, B) → base_1
  27. Segment(B, C) → base_2
  28. Angle(I, L, C) → α
  29. Angle(K, G, B) → γ
  30. Midpoint(b) → D
  31. Rotate(A, 180°, D) → A'_2
  32. Rotate(B, 180°, D) → B'
  33. Rotate(C, 180°, D) → C'_1
  34. Polygon(A'_2, B', C'_1) → t1', c'_3, a'_3, b'_3
  35. Line(C, B') → j
  36. OrthogonalLine(M, c) → k
  37. Intersect(k, j) → H
  38. Segment(M, H) → height_1
  39. Angle(H, M, A) → β