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Special Quadrilateral Theorem 1

Special Quadrilateral Theorem 1
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2017-02-09 03:40
PolygonTransformationGeometric Construction
In collections Congruence (CO) Cluster Congruence (Vol 2) CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Gail LeBlancCCSS High School: Geometry (Congruence) Volume 2 Unit 7: Polygons and Quadrilaterals Quadrilaterals
This example demonstrates Theorem 1 of special quadrilaterals, involving concepts such as rotation, lines, and circles. Using commands like Rotate, Line, Circle, etc., it dynamically illustrates the properties of quadrilaterals. Suitable for middle school and above students to learn geometric transformations and properties of quadrilaterals.

GeoGebra Commands & Parameters

  1. Rotate(B, a°, A) → B'
  2. Angle(B, A, B') → α
  3. Ray(A, B) → f
  4. Ray(A, B') → g
  5. Line(B, g) → h
  6. Point(g) → C
  7. Line(C, f) → i
  8. Intersect(h, i) → D
  9. Segment(C, D) → j
  10. Segment(A, B) → k
  11. Segment(B, D) → l
  12. Segment(A, C) → m
  13. Min(m, k) → b
  14. Circle(C, (0.2 * b)) → d
  15. Circle(A, (0.2 * b)) → e
  16. Circle(B, (0.2 * b)) → p
  17. Circle(D, (0.2 * b)) → c
  18. Intersect(e, k, 1) → E
  19. Intersect(e, m, 1) → F
  20. Intersect(p, k, 1) → G
  21. Intersect(p, l, 1) → H
  22. Intersect(d, g, 2) → I
  23. Ray(C, I) → q
  24. Intersect(c, h, 2) → J
  25. Ray(D, J) → r
  26. Intersect(c, i, 2) → K
  27. Ray(D, K) → s
  28. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], B) → A'
  29. Segment(A, A') → t
  30. Rotate(E, If[1 < o ≤ 2, ((o - 1) * α), α], A) → E'
  31. Dilate(A, If[1 < o ≤ 2, 2 - o, 0], C) → A'_1
  32. Vector(A, A'_1) → u
  33. Segment(A, A'_1) → f_1
  34. Dilate(C, If[2 < o ≤ 3, 3 - o, 0], D) → C'
  35. Vector(C, C') → v
  36. Segment(C, C') → g_1
  37. Dilate(D, If[3 < o ≤ 4, 4 - o, 0], B) → D'
  38. Segment(D, D') → h_1
  39. Polygon(A, B, D, C) → poly1, a_1, b_1, d_2, c_2
  40. Dilate(A, If[5.5 < o ≤ 6.5, 6.5 - o, 0], C) → A'_2
  41. Vector(A, A'_2) → w
  42. Translate(A, w) → A'_3
  43. Translate(A', w) → A''
  44. Dilate(A, If[5 < o ≤ 6, 6 - o, 0], B) → A'_4
  45. Vector(A, A'_4) → u_1
  46. Translate(A, u_1) → A'_5
  47. Translate(A'_1, u_1) → L
  48. Segment(A'_5, L) → i_1
  49. Dilate(A, If[4 < o ≤ 5, 5 - o, 0], C) → A'_6
  50. Vector(A, A'_6) → v_1
  51. Translate(A, v_1) → A'_7
  52. Translate(A', v_1) → A''_1
  53. Segment(A'_7, A''_1) → t'_1
  54. Rotate(E, If[6.5 < o ≤ 7.5, ((o - 6.5) * α), α], A) → E'_1
  55. CircleSector(A, E, E'_1) → c_1
  56. Dilate(A, If[7.5 < o ≤ 8.5, 8.5 - o, 0], C) → A'_8
  57. Vector(A, A'_8) → w_1
  58. Translate(c_1, w_1) → d_1
  59. Dilate(C, If[8.5 < o ≤ 9.5, 9.5 - o, 0], D) → C'_1
  60. Vector(C, C'_1) → e_1
  61. Translate(d_1, e_1) → k_1