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Parallelogram Theorem

Parallelogram Theorem
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2016-10-16 05:59
PolygonAngleTransformation
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 Gail LeBlancCCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Unit 7: Polygons and Quadrilaterals Quadrilaterals
This example illustrates the parallelogram theorem through a graphical representation. Key mathematical concepts include the properties of parallelograms. Constructed using GeoGebra commands such as rotation, angle, line, and segment, it is suitable for students in middle school and above to learn geometric construction.

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. CircleSector(A, E, E') → c_1
  32. Dilate(A, If[2 < o ≤ 3, 3 - o, 0], C) → A'_1
  33. Vector(A, A'_1) → u
  34. Translate(c_1, u) → d_1
  35. Segment(A, A'_1) → f_1
  36. Dilate(C, If[3 < o ≤ 4, 4 - o, 0], D) → C'
  37. Vector(C, C') → v
  38. Translate(d_1, v) → e_1
  39. Segment(C, C') → g_1
  40. Dilate(D, If[4 < o ≤ 5, 5 - o, 0], B) → D'
  41. Segment(D, D') → h_1
  42. Polygon(A, B, D, C) → poly1, a_1, b_1, d_2, c_2
  43. Dilate(A, If[5.5 < o ≤ 6.5, 6.5 - o, 0], C) → A'_2
  44. Vector(A, A'_2) → w
  45. Translate(A, w) → A'_3
  46. Translate(A', w) → A''
  47. Segment(A'_3, A'') → t'
  48. Dilate(A, If[6.5 < o ≤ 7.5, 7.5 - o, 0], B) → A'_4
  49. Vector(A, A'_4) → u_1
  50. Translate(A, u_1) → A'_5
  51. Translate(A'_1, u_1) → L
  52. Segment(A'_5, L) → i_1