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Similar Rectangles on the Sides of a Right Triangle

Similar Rectangles on the Sides of a Right Triangle
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2015-08-31 10:29
TrianglePolygonGeometric Construction
This example demonstrates constructing similar rectangles on the sides of a right triangle, revealing area relationships and connections to the Pythagorean theorem. Key math concepts include similar figures, Pythagorean theorem, area calculation, and proportional relationships. GeoGebra commands and objects used are segment, orthogonal line, point, circle, intersect, polygon, and LaTeX. Suitable for high school mathematics teaching to understand applications of similarity and the Pythagorean theorem.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. OrthogonalLine(A, a) → b
  3. Point(b) → C
  4. Segment(C, A) → c
  5. Segment(C, B) → d
  6. Circle(C, d / 3) → e
  7. OrthogonalLine(C, d) → f
  8. Intersect(e, f) → D, E
  9. Segment(C, E) → g
  10. OrthogonalLine(E, g) → h
  11. OrthogonalLine(B, d) → i
  12. Intersect(i, h) → F
  13. Segment(E, F) → j
  14. Segment(B, F) → k
  15. Circle(C, c / 3) → p
  16. OrthogonalLine(C, c) → l
  17. Intersect(p, l) → G, H
  18. Segment(G, C) → m
  19. OrthogonalLine(G, m) → n
  20. OrthogonalLine(A, c) → q
  21. Intersect(n, q) → I
  22. Segment(G, I) → r
  23. Segment(I, A) → s
  24. OrthogonalLine(A, a) → t
  25. Circle(A, a / 3) → c_1
  26. Intersect(c_1, t) → J, K
  27. Segment(A, J) → a_1
  28. OrthogonalLine(J, a_1) → b_1
  29. OrthogonalLine(B, a) → d_1
  30. Intersect(b_1, d_1) → L
  31. Segment(B, L) → e_1
  32. Segment(L, J) → f_1
  33. Polygon(C, B, F, E) → S, c_2, b_2, f_2, e_2
  34. LaTeX(S, true, true) → text1
  35. Polygon(C, G, I, A) → Q, c_3, g_1, i_1, a_2
  36. LaTeX(Q, true, true) → text2
  37. Polygon(A, J, L, B) → R, a_3, j_1, l_1, b_3
  38. LaTeX(R, true, true) → text3
  39. LaTeX(SumQplusR, true, true) → text4