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Two Squares and Two Triangles

Two Squares and Two Triangles
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2017-02-19 21:08
PolygonTransformationGeometric Construction
This example demonstrates geometric relationships formed by two squares and two triangles, involving concepts like geometric transformations, ellipses, arithmetic mean, hypothesis testing, and surface area. Construction highlights GeoGebra commands: Intersect, Point, Polygon, If, Translate. Suitable for high school and above learners exploring geometric transformations and spatial relations.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  4. Polygon(C, E, 4) → poly2, j, k, l, m, F, G
  5. Polygon(C, D, G) → poly3, g_1, c, d
  6. Polygon(C, B, E) → poly4, e, c_1, b
  7. If(0 ≤ a < 1, Polygon[Rotate[C, (((-π)) / 2 * (a - 0)), C], Rotate[D, (((-π)) / 2 * (a - 0)), C], Rotate[G, (((-π)) / 2 * (a - 0)), C]], Polygon[Rotate[C, ((-π)) / 2, C], Rotate[D, ((-π)) / 2, C], Rotate[G, ((-π)) / 2, C]]) → poly5
  8. If(1 ≤ a ≤ 2, Dilate[C, 2 - a, B], Dilate[C, 0, C]) → H
  9. Translate(H, Vector[B, C]) → H'
  10. Polygon(E, H, H') → poly6, h', e_1, h_1