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Rectangle Perimeter-Diagonal Relationship Demo

Rectangle Perimeter-Diagonal Relationship Demo
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2015-10-29 20:57
PolygonFunctionTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the dynamic relationship between a rectangle's perimeter, diagonal, and angles. It involves core math concepts like perimeter calculation, diagonal properties, trigonometric function application, and analytical geometry plotting. Constructed using GeoGebra commands such as Intersect, Point, Segment, Rotate, OrthogonalLine, Polygon, and Circle, it is suitable for high school mathematics education, focusing on geometric transformations, trigonometry, and analytical geometry integration.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(Circle[(0, 0), a]) → B
  3. Segment((0, 0), B) → b
  4. Rotate(b, α, A) → b'
  5. Rotate(B, α, A) → B'
  6. OrthogonalLine(B', yAxis) → c
  7. OrthogonalLine(B', xAxis) → d
  8. Intersect(c, e) → C
  9. Intersect(d, f) → D
  10. Polygon(C, B', D, A) → poly1, c_1, b'_1, d_1, a_1
  11. Circle(A, a) → g
  12. Intersect(g, h, 1) → E
  13. Intersect(g, h, 2) → F