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Exploring the Trapezoid

Exploring the Trapezoid
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2017-04-06 07:46
PolygonAngleCoordinate GeometryGeometric Construction
This example demonstrates the geometric properties and transformations of a trapezoid. It involves core mathematical concepts such as polygons, angles, rotation, coordinate geometry, and geometric construction. Key GeoGebra commands used include Line, Angle, Rotate, Intersect, OrthogonalLine, Polygon, Segment, and Midpoint to construct the trapezoid and related elements. Suitable for high school mathematics teaching and geometric learning, helping students understand the basic properties and applications of trapezoids through transformations.

GeoGebra Commands & Parameters

  1. Line(A, B) → f
  2. Line(C, f) → g
  3. Line(A, C) → h
  4. Angle(f, h) → α
  5. Rotate(A, (-α), B) → A'
  6. Angle(A', B, A) → β
  7. Line(A', B) → i
  8. Intersect(g, i) → D
  9. OrthogonalLine(C, f) → j
  10. Intersect(f, j) → E
  11. Polygon(C, D, B, A) → poly1, c, d, b, a
  12. Segment(C, E) → k
  13. Midpoint(a) → F
  14. Midpoint(d) → G
  15. Segment(F, G) → l
  16. Angle(A, C, D) → γ
  17. Angle(C, D, B) → δ