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Demonstrating Equal Areas of Parallelograms

Demonstrating Equal Areas of Parallelograms
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2014-10-27 03:25
TrianglePolygonVectorGeometric Construction
This example uses congruent triangles to demonstrate that red and blue parallelograms always have the same area. It involves core math concepts like congruent triangles, parallelogram area formulas, and vector operations. Construction uses commands such as Point, Segment, Vector, Line, Intersect, Polygon, with objects like u, c, d, e for vectors and poly1, poly2 for parallelograms. Suitable for middle school and above to understand parallelogram area properties and congruent triangle applications.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Segment(A, B) → a
  3. Vector(A, B) → u
  4. Line(C, u) → c
  5. Segment(A, C) → d
  6. Line(B, d) → e
  7. Intersect(c, e) → D
  8. Segment(B, D) → f
  9. Segment(D, C) → g
  10. Segment(B, C) → h
  11. Point(h) → E
  12. Line(E, a) → i
  13. Line(E, f) → j
  14. Intersect(j, a) → F
  15. Intersect(i, f) → G
  16. Intersect(j, g) → I
  17. Segment(F, I) → l
  18. Polygon(B, F, E, G) → poly2, b_1, f_2, e_2, g_1
  19. Polygon(G, D, I, E) → poly3, g_2, d_1, i_1, e_3
  20. Intersect(i, d) → H
  21. Polygon(F, E, H, A) → poly1, f_1, e_1, h_1, a_1
  22. Polygon(E, H, C, I) → poly4, e_4, h_2, c_1, i_2