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Animation Demonstrating Pyramid, LCM, GCD, Symmetry, and Kite

Animation Demonstrating Pyramid, LCM, GCD, Symmetry, and Kite
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2016-06-18 08:50
Solid GeometryGeometric 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 CCSS High School: Geometry (Congruence) Volume 2
This example demonstrates geometric concepts such as pyramids, LCM (Least Common Multiple), GCD (Greatest Common Divisor), symmetry, and kites through animation. It involves core mathematical ideas including geometric representations of LCM and GCD, symmetry transformations, kite properties, and multiplication principles. The construction uses GeoGebra commands like Line, OrthogonalLine, Point, Ray, Midpoint, Segment, Circle, Intersect, CircleSector, Polygon, Rotate, Dilate, and Angle. Suitable for high school mathematics education to visually illustrate geometric transformations and algebraic applications.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. OrthogonalLine(A, a) → d
  3. OrthogonalLine(B, a) → e
  4. Point(d) → C
  5. Ray(A, C) → c
  6. Point(d) → E
  7. Ray(A, E) → b
  8. Ray(A, B) → g
  9. Point(g) → F
  10. Ray(A, F) → h
  11. Point(h) → G
  12. Ray(A, E) → i
  13. Point(i) → H
  14. Midpoint(H, G) → D
  15. Segment(A, H) → j
  16. Segment(A, G) → k
  17. Circle(A, Min[(0.15 * j), (0.15 * k)]) → p
  18. Intersect(p, a, 2) → I
  19. Intersect(p, i, 1) → J
  20. Intersect(p, a, 1) → K
  21. CircleSector(A, J, K) → q
  22. Polygon(A, G, H) → poly1, h_1, a_1, g_1
  23. Rotate(q, If[0 < f ≤ 1, ((-f) * π / 2), -1.5707963267948966], A) → q'
  24. Dilate(G, If[1 < f ≤ 2, 2 - f, 0], D) → G'
  25. Segment(G, G') → l
  26. Rotate(G, If[2 < f ≤ 3, ((f - 2) * π), 3.141592653589793], D) → G'_1
  27. Rotate(G', If[2 < f ≤ 3, ((f - 2) * π), 3.141592653589793], D) → G''
  28. Segment(G'_1, G'') → l'
  29. Angle(H, D, A) → α
  30. Rotate(G'_1, If[3 < f ≤ 4, ((f - 3) * α), α], D) → L
  31. Rotate(G'', If[3 < f ≤ 4, ((f - 3) * α), α], D) → G'''
  32. Segment(L, G''') → l''