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Exploring Similar Quadrilaterals by John Golden

Exploring Similar Quadrilaterals by John Golden
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2015-12-08 22:28
PolygonTrigonometryGeometric Construction
This example demonstrates the properties and transformations of similar quadrilaterals. It involves similarity, geometric transformations, and properties of quadrilaterals. Using GeoGebra commands such as quadsame, twostage, and Polygon, you can dynamically explore the similarity of quadrilaterals. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. quadsame(A, B, C, D, D, C) → poly2, I, J
  2. quadsame(D, A, B, C, C, B) → poly3, K, L
  3. quadsame(B, C, D, A, A, D) → poly1, E, F
  4. quadsame(C, D, A, B, B, A) → poly4, G, H
  5. quadsame(A, B, C, D, I, J) → poly5, M, N
  6. quadsame(D, A, B, C, K, L) → poly6, O, P
  7. quadsame(C, D, A, B, G, H) → poly7, Q, R
  8. quadsame(B, C, D, A, E, F) → poly8, S, T
  9. twostage(I, J, N, M) → poly9, poly10, A_1, B_1, C_1, D_1, E_1, F_1, G_1, H_1, poly11, poly12, poly13, poly14, U, V, W, Z
  10. twostage(K, L, P, O) → poly15, poly16, M_1, N_1, O_1, P_1, Q_1, R_1, S_1, T_1, poly17, poly18, poly19, poly20, I_1, J_1, K_1, L_1
  11. twostage(G, H, R, Q) → poly21, poly22, A_2, B_2, C_2, D_2, E_2, F_2, G_2, H_2, poly23, poly24, poly25, poly26, U_1, V_1, W_1, Z_1
  12. twostage(E, F, T, S) → poly27, poly28, M_2, N_2, O_2, P_2, Q_2, R_2, S_2, T_2, poly29, poly30, poly31, poly32, I_2, J_2, K_2, L_2
  13. twostage(I_2, J_2, P_2, O_2) → poly33, poly34, A_3, B_3, C_3, D_3, E_3, F_3, G_3, H_3, poly35, poly36, poly37, poly38, U_2, V_2, W_2, Z_2
  14. twostage(U_1, V_1, D_2, C_2) → poly39, poly40, M_3, N_3, O_3, P_3, Q_3, R_3, S_3, T_3, poly41, poly42, poly43, poly44, I_3, J_3, K_3, L_3
  15. twostage(U, V, D_1, C_1) → poly45, poly46, A_4, B_4, C_4, D_4, E_4, F_4, G_4, H_4, poly47, poly48, poly49, poly50, U_3, V_3, W_3, Z_3
  16. twostage(I_1, J_1, P_1, O_1) → poly51, poly52, M_4, N_4, O_4, P_4, Q_4, R_4, S_4, T_4, poly53, poly54, poly55, poly56, I_4, J_4, K_4, L_4
  17. twostage(I_4, J_4, P_4, O_4) → poly57, poly58, A_5, B_5, C_5, D_5, E_5, F_5, G_5, H_5, poly59, poly60, poly61, poly62, U_4, V_4, W_4, Z_4
  18. twostage(K_4, L_4, R_4, Q_4) → poly63, poly64, M_5, N_5, O_5, P_5, Q_5, R_5, S_5, T_5, poly65, poly66, poly67, poly68, I_5, J_5, K_5, L_5
  19. twostage(M_4, N_4, T_4, S_4) → poly69, poly70, A_6, B_6, C_6, D_6, E_6, F_6, G_6, H_6, poly71, poly72, poly73, poly74, U_5, V_5, W_5, Z_5
  20. twostage(I_3, J_3, P_3, O_3) → poly75, poly76, M_6, N_6, O_6, P_6, Q_6, R_6, S_6, T_6, poly77, poly78, poly79, poly80, I_6, J_6, K_6, L_6
  21. twostage(M_3, N_3, T_3, S_3) → poly81, poly82, A_7, B_7, C_7, D_7, E_7, F_7, G_7, H_7, poly83, poly84, poly85, poly86, U_6, V_6, W_6, Z_6
  22. twostage(K_3, L_3, R_3, Q_3) → poly87, poly88, M_7, N_7, O_7, P_7, Q_7, R_7, S_7, T_7, poly89, poly90, poly91, poly92, I_7, J_7, K_7, L_7
  23. twostage(A_3, B_3, H_3, G_3) → poly93, poly94, A_8, B_8, C_8, D_8, E_8, F_8, G_8, H_8, poly95, poly96, poly97, poly98, U_7, V_7, W_7, Z_7
  24. twostage(U_2, V_2, D_3, C_3) → poly99, poly100, M_8, N_8, O_8, P_8, Q_8, R_8, S_8, T_8, poly101, poly102, poly103, poly104, I_8, J_8, K_8, L_8
  25. twostage(A_4, B_4, H_4, G_4) → poly105, poly106, A_9, B_9, C_9, D_9, E_9, F_9, G_9, H_9, poly107, poly108, poly109, poly110, U_8, V_8, W_8, Z_8
  26. twostage(W_2, Z_2, F_3, E_3) → poly111, poly112, M_9, N_9, O_9, P_9, Q_9, R_9, S_9, T_9, poly113, poly114, poly115, poly116, I_9, J_9, K_9, L_9
  27. twostage(W_3, Z_3, F_4, E_4) → poly117, poly118, A_{10}, B_{10}, C_{10}, D_{10}, E_{10}, F_{10}, G_{10}, H_{10}, poly119, poly120, poly121, poly122, U_9, V_9, W_9, Z_9
  28. twostage(U_3, V_3, D_4, C_4) → poly123, poly124, M_{10}, N_{10}, O_{10}, P_{10}, Q_{10}, R_{10}, S_{10}, T_{10}, poly125, poly126, poly127, poly128, I_{10}, J_{10}, K_{10}, L_{10}
  29. twostage(I_6, J_6, P_6, O_6) → poly129, poly130, A_{11}, B_{11}, C_{11}, D_{11}, E_{11}, F_{11}, G_{11}, H_{11}, poly131, poly132, poly133, poly134, U_{10}, V_{10}, W_{10}, Z_{10}
  30. twostage(U_{10}, V_{10}, D_{11}, C_{11}) → poly135, poly136, M_{11}, N_{11}, O_{11}, P_{11}, Q_{11}, R_{11}, S_{11}, T_{11}, poly137, poly138, poly139, poly140, I_{11}, J_{11}, K_{11}, L_{11}
  31. twostage(I_{10}, J_{10}, P_{10}, O_{10}) → poly141, poly142, A_{12}, B_{12}, C_{12}, D_{12}, E_{12}, F_{12}, G_{12}, H_{12}, poly143, poly144, poly145, poly146, U_{11}, V_{11}, W_{11}, Z_{11}
  32. twostage(A_{12}, B_{12}, H_{12}, G_{12}) → poly147, poly148, M_{12}, N_{12}, O_{12}, P_{12}, Q_{12}, R_{12}, S_{12}, T_{12}, poly149, poly150, poly151, poly152, I_{12}, J_{12}, K_{12}, L_{12}
  33. twostage(I_{12}, J_{12}, P_{12}, O_{12}) → poly153, poly154, A_{13}, B_{13}, C_{13}, D_{13}, E_{13}, F_{13}, G_{13}, H_{13}, poly155, poly156, poly157, poly158, U_{12}, V_{12}, W_{12}, Z_{12}
  34. twostage(K_{11}, L_{11}, R_{11}, Q_{11}) → poly159, poly160, M_{13}, N_{13}, O_{13}, P_{13}, Q_{13}, R_{13}, S_{13}, T_{13}, poly161, poly162, poly163, poly164, I_{13}, J_{13}, K_{13}, L_{13}
  35. Polygon(A, B, C, D) → poly165, a, b, c, d
  36. twostage(A_{13}, B_{13}, H_{13}, G_{13}) → poly166, poly167, A_{14}, B_{14}, C_{14}, D_{14}, E_{14}, F_{14}, G_{14}, H_{14}, poly168, poly169, poly170, poly171, U_{13}, V_{13}, W_{13}, Z_{13}
  37. twostage(L_6, R_6, Q_6, K_6) → poly172, poly173, M_{14}, N_{14}, O_{14}, P_{14}, Q_{14}, R_{14}, S_{14}, T_{14}, poly174, poly175, poly176, poly177, I_{14}, J_{14}, K_{14}, L_{14}
  38. twostage(J_7, P_7, O_7, I_7) → poly178, poly179, A_{15}, B_{15}, C_{15}, D_{15}, E_{15}, F_{15}, G_{15}, H_{15}, poly180, poly181, poly182, poly183, U_{14}, V_{14}, W_{14}, Z_{14}
  39. twostage(Z_7, F_8, E_8, W_7) → poly184, poly185, M_{15}, N_{15}, O_{15}, P_{15}, Q_{15}, R_{15}, S_{15}, T_{15}, poly186, poly187, poly188, poly189, I_{15}, J_{15}, K_{15}, L_{15}
  40. twostage(Z_{14}, F_{15}, E_{15}, W_{14}) → poly190, poly191, A_{16}, B_{16}, C_{16}, D_{16}, E_{16}, F_{16}, G_{16}, H_{16}, poly192, poly193, poly194, poly195, U_{15}, V_{15}, W_{15}, Z_{15}
  41. twostage(K_{14}, L_{14}, R_{14}, Q_{14}) → poly196, poly197, M_{16}, N_{16}, O_{16}, P_{16}, Q_{16}, R_{16}, S_{16}, T_{16}, poly198, poly199, poly200, poly201, I_{16}, J_{16}, K_{16}, L_{16}
  42. twostage(M_{16}, N_{16}, T_{16}, S_{16}) → poly202, poly203, A_{17}, B_{17}, C_{17}, D_{17}, E_{17}, F_{17}, G_{17}, H_{17}, poly204, poly205, poly206, poly207, U_{16}, V_{16}, W_{16}, Z_{16}
  43. twostage(W_{13}, Z_{13}, F_{14}, E_{14}) → poly208, poly209, M_{17}, N_{17}, O_{17}, P_{17}, Q_{17}, R_{17}, S_{17}, T_{17}, poly210, poly211, poly212, poly213, I_{17}, J_{17}, K_{17}, L_{17}
  44. twostage(M_{17}, N_{17}, T_{17}, S_{17}) → poly214, poly215, A_{18}, B_{18}, C_{18}, D_{18}, E_{18}, F_{18}, G_{18}, H_{18}, poly216, poly217, poly218, poly219, U_{17}, V_{17}, W_{17}, Z_{17}