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Pythagorean Theorem Demonstration by GaëlleJ

Pythagorean Theorem Demonstration by GaëlleJ
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2013-03-12 04:04
TriangleCircleVectorGeometric Construction
This example demonstrates the Pythagorean theorem in right-angled triangles, illustrating the relationship between the lengths of the sides. Key math concepts include the Pythagorean theorem, right triangles, vectors, and geometric transformations. The construction utilizes GeoGebra commands/objects such as Segment, OrthogonalLine, Point, Polygon, AngularBisector, Intersect, Vector, Translate, and Circle. It is suitable for middle school students and above for learning geometric constructions and theorem verification, as well as for classroom demonstrations.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. OrthogonalLine(B, a) → b
  3. Point(b) → C
  4. Segment(B, C) → c
  5. Polygon(A, C, B) → veelhoek1, b_1, a_1, c_1
  6. Polygon(A, C, 4) → veelhoek2, a_2, c_2, d, e, D, E
  7. Polygon(C, B, 4) → veelhoek3, c_3, b_2, f, g, F, G
  8. Polygon(B, A, 4) → veelhoek4, b_3, a_3, h, i, H, I
  9. AngularBisector(a, c) → j, k
  10. Intersect(k, b_1) → J
  11. OrthogonalLine(J, c) → l
  12. OrthogonalLine(J, a) → m
  13. Intersect(m, a) → K
  14. Intersect(b, l) → L
  15. Polygon(K, J, L, B) → veelhoek5, k_1, j_1, l_1, b_4
  16. OrthogonalLine(A, a) → n
  17. Intersect(l, n) → M
  18. Polygon(A, M, J) → veelhoek6, j_2, a_4, m_1
  19. Intersect(l, e) → N
  20. Polygon(N, M, A) → veelhoek7, a_5, n_1, m_2
  21. OrthogonalLine(D, a_4) → p
  22. Intersect(l, p) → S
  23. OrthogonalLine(N, c_2) → q
  24. OrthogonalLine(J, q) → r
  25. Intersect(p, q) → O
  26. Intersect(q, c_2) → P
  27. Polygon(J, O, P, C) → veelhoek8, j_3, o, p_1, c_4
  28. Vector(O, L) → u
  29. Translate(J, u) → J'
  30. Translate(O, u) → O'
  31. Translate(P, u) → P'
  32. Translate(C, u) → C'
  33. Polygon(J', O', P', C') → veelhoek8', j', o', p', c'
  34. Intersect(r, d) → Q
  35. Polygon(N, E, Q, O) → veelhoek9, n_2, e_1, q_1, o_1
  36. Vector(Q, K) → v
  37. Translate(N, v) → N'
  38. Translate(E, v) → E'
  39. Translate(Q, v) → Q'
  40. Translate(O, v) → O'_1
  41. Polygon(N', E', Q', O'_1) → veelhoek9', n', e', q', o'_1
  42. OrthogonalLine(Q, p) → s
  43. OrthogonalLine(P, p) → t
  44. Intersect(p, s) → R
  45. Intersect(p, t) → T
  46. Polygon(Q, R, D) → veelhoek10, d_1, q_2, r_1
  47. Polygon(P, T, O) → veelhoek11, o_2, p_2, t_1
  48. Polygon(P, T, D) → veelhoek12, d_2, p_3, t_2
  49. Polygon(R, Q, O) → veelhoek13, o_3, r_2, q_3
  50. Polygon(S, N, O) → veelhoek14, o_4, s_1, n_3
  51. Polygon(J, S, O) → veelhoek15, o_5, j_4, s_2
  52. Polygon(K, A, E') → veelhoek16, e'_1, k_2, a_6
  53. Polygon(B, K, O'_1) → veelhoek17, o'_2, b_5, k_3
  54. Polygon(E', H, N') → veelhoek18, n'_1, e'_2, h_1
  55. Polygon(N', I, O'_1) → veelhoek19, o'_3, n'_2, i_1
  56. Polygon(J', B, L) → veelhoek20, l_2, j'_1, b_6
  57. Polygon(L, C, P') → veelhoek21, p'_1, l_3, c_5
  58. Polygon(P', G, C') → veelhoek22, c'_1, p'_2, g_1
  59. Polygon(C', J', F) → veelhoek23, f_1, c'_2, j'_2
  60. Segment(E', E) → e_2
  61. Circle(E', verschuiving * Distance[E', E]) → f_2
  62. Intersect(f_2, e_2, 1) → U
  63. Vector(E', U) → w
  64. Translate(N', w) → N''
  65. Translate(E', w) → E''
  66. Translate(Q', w) → Q''
  67. Translate(O'_1, w) → V
  68. Polygon(N'', E'', Q'', V) → veelhoek9'', n'', e'', q'', v_1
  69. Segment(P', P) → g_2
  70. Circle(P', verschuiving * Distance[P', P]) → h_2
  71. Intersect(h_2, g_2, 1) → W
  72. Vector(P', W) → z
  73. Translate(L, z) → L'
  74. Translate(C, z) → C'_1
  75. Translate(P', z) → P''
  76. Polygon(L', C'_1, P'') → veelhoek21', p'', l', c'_3
  77. Segment(C', D) → i_2
  78. Circle(C', verschuiving * Distance[C', D]) → d_3
  79. Intersect(d_3, i_2, 1) → Z
  80. Vector(C', Z) → u_1
  81. Translate(C', u_1) → C''
  82. Translate(J', u_1) → J''
  83. Translate(F, u_1) → F'
  84. Polygon(C'', J'', F') → veelhoek23', f', c'', j''
  85. Segment(J', J) → e_3
  86. Circle(J', verschuiving * Distance[J', J]) → f_3
  87. Intersect(f_3, e_3, 1) → A_1
  88. Vector(J', A_1) → w_1
  89. Translate(J', w_1) → J''_1
  90. Translate(B, w_1) → B'
  91. Translate(L, w_1) → L'_1
  92. Polygon(J''_1, B', L'_1) → veelhoek20', l'_1, j''_1, b'
  93. Segment(P', N) → g_3
  94. Circle(P', verschuiving * Distance[P', N]) → h_3
  95. Intersect(h_3, g_3, 1) → B_1
  96. Vector(P', B_1) → z_1
  97. Translate(P', z_1) → P''_1
  98. Translate(G, z_1) → G'
  99. Translate(C', z_1) → C''_1
  100. Polygon(P''_1, G', C''_1) → veelhoek22', c''_1, p''_1, g'
  101. Translate(J', z) → J''_2
  102. Translate(O', z) → O''
  103. Translate(P', z) → P''_2
  104. Translate(C', z) → C''_2
  105. Polygon(J''_2, O'', P''_2, C''_2) → veelhoek8'', j''_2, o'', p''_2, c''_2
  106. Segment(K, Q) → i_3
  107. Circle(K, verschuiving * Distance[Q', Q]) → r_3
  108. Intersect(q'', e'') → C_1
  109. Vector(K, Q'') → u_2
  110. Translate(B, u_2) → B'_1
  111. Translate(K, u_2) → K'
  112. Translate(O'_1, u_2) → D_1
  113. Polygon(B'_1, K', D_1) → veelhoek17', d_4, b'_1, k'
  114. Segment(H, T) → m_3
  115. Circle(H, verschuiving * Distance[H, T]) → s_3
  116. Intersect(a_2, m_1) → E_1
  117. Intersect(a_2, m_1) → F_1
  118. Intersect(a_2, m_1) → G_1
  119. Intersect(s_3, m_3, 1) → H_1
  120. Vector(H, H_1) → v_2
  121. Translate(E', v_2) → E''_1
  122. Translate(H, v_2) → H'
  123. Translate(N', v_2) → N''_1
  124. Polygon(E''_1, H', N''_1) → veelhoek18', n''_1, e''_1, h'
  125. Segment(I, S) → t_3
  126. Circle(I, verschuiving * Distance[I, S]) → e_4
  127. Intersect(e_4, t_3, 1) → I_1
  128. Vector(I, I_1) → w_2
  129. Translate(N', w_2) → N''_2
  130. Translate(I, w_2) → I'
  131. Translate(O'_1, w_2) → J_1
  132. Polygon(N''_2, I', J_1) → veelhoek19', j_5, n''_2, i'
  133. Segment(A, M) → f_4
  134. Segment(E', A) → g_4
  135. Circle(E', verschuiving * Distance[E', A]) → h_4
  136. Intersect(a_3, k_2) → K_1
  137. Intersect(a_3, k_2) → L_1
  138. Intersect(a_3, k_2) → M_1
  139. Intersect(a_3, k_2) → N_1
  140. Intersect(a_3, k_2) → O_1
  141. Intersect(h_4, a_3, 1) → P_1
  142. Vector(E', P_1) → z_2
  143. Translate(K, z_2) → K'_1
  144. Translate(A, z_2) → A'
  145. Translate(E', z_2) → E''_2
  146. Polygon(K'_1, A', E''_2) → veelhoek16', e''_2, k'_1, a'

AI Drawing Prompt Reference

Draw a right-angled triangle and label the lengths of its two legs. Demonstrate the Pythagorean theorem by constructing and rotating these sides to form various shapes. Start by drawing the right-angled triangle, then create perpendicular lines and use vectors to construct new figures. Translate and rotate these shapes to form multiple interconnected polygons, visually illustrating the relationship between the sides as described by the Pythagorean theorem.
The prompt above was compiled from the original drawing commands and is for reference only.