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Two Squares and Three Triangles Area Problem

Two Squares and Three Triangles Area Problem
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2017-04-15 02:07
TrianglePolygonGeometric Construction
This example demonstrates the relationship between the areas of two squares and three triangles. Key mathematical concepts include area calculation, similarity transformation, and quadratic equations. Using GeoGebra commands such as Point, Polygon, Segment, etc., these geometric shapes can be constructed. Suitable for students at the junior high school level and above to learn geometry and algebra.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  4. Point(g) → E
  5. Polygon(E, B, 4) → poly2, j, k, l, m, F, G
  6. Segment(A, E) → n
  7. OrthogonalLine(E, n) → p
  8. Intersect(p, k) → I
  9. Line(G, F) → q
  10. Polygon(A, E, C) → poly3, c, a, e
  11. Polygon(I, F, E) → poly4, e_1, i_1, f_1
  12. Intersect(p, q) → H
  13. Polygon(A, I, H) → poly5, h_1, a_1, i_2
  14. Line(C, p) → r
  15. Angle(A, E, I) → α
  16. Segment(F, H) → s
  17. If(2 ≤ b < 3, Polygon[I, E, Dilate[F, 3 - b, C]], Polygon[E, I, C]) → poly6
  18. Line(H, k) → t
  19. Line(C, B) → d
  20. Intersect(t, d) → J
  21. If(4 ≤ b < 5, Polygon[I, Dilate[E, 5 - b, J], Dilate[C, 5 - b, B]], Polygon[I, B, J]) → poly7
  22. If(4 ≤ b < 5, Polygon[A, Dilate[E, 5 - b, J], Dilate[C, 5 - b, B]], Polygon[A, B, J]) → poly8
  23. If(6 ≤ b < 7, Polygon[I, B, Dilate[J, 7 - b, H]], Polygon[I, B, H]) → poly9
  24. If(6 ≤ b < 7, Polygon[A, B, Dilate[J, 7 - b, H]], Polygon[A, B, H]) → poly10
  25. PolyLine(A, E, I) → g_1