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Distributive Property with Rectangles

Distributive Property with Rectangles
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2020-04-17 01:21
Geometric Construction
This example demonstrates the distributive property geometrically using dynamic rectangles, visually showing that a(b+c) equals the sum of two areas. Core concepts include distributive property, area calculation, and the integration of algebra and geometry. Constructed with GeoGebra commands like Segment, OrthogonalLine, Intersect, Polygon, and Vector, it is suitable for middle school students and above to understand algebraic properties and for mathematical visualization teaching.

GeoGebra Commands & Parameters

  1. Segment(A, D) → c1
  2. Segment(A, B) → a1
  3. Segment(B, C) → b1
  4. Segment(D, E) → d1
  5. OrthogonalLine(B, a1) → j
  6. OrthogonalLine(D, c1) → k
  7. OrthogonalLine(E, d1) → l
  8. OrthogonalLine(C, b1) → m
  9. Intersect(l, m) → F
  10. Intersect(j, l) → G
  11. Intersect(j, k) → H
  12. Intersect(k, m) → I
  13. Segment(E, G) → q
  14. Polygon(C, A, E, F) → q1, c_1, f_8, e_1, f_2
  15. Polygon(A, D, H, B) → q2, a_2, d_1, h_1, b_1
  16. Polygon(B, C, I, H) → q3, b_2, c_2, i_1, h_2
  17. Polygon(D, E, G, H) → q4, d_2, e_2, g_1, h_3
  18. Polygon(H, G, F, I) → q5, h_4, g_2, f_3, i_2
  19. Vector(T, U) → u
  20. Vector(J, K) → v
  21. Vector(L, M) → w
  22. Vector(N, O) → e
  23. Vector(P, Q) → p
  24. Segment(U, Q) → r
  25. Segment(C, I) → i
  26. Segment(B, H) → s
  27. Segment(I, H) → t
  28. Segment(D, H) → f_1
  29. Segment(G, F) → j_1
  30. Segment(I, F) → k_1
  31. Segment(H, G) → l_1