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Dynamic Demonstration of Trapezoid Area via Rotation

Dynamic Demonstration of Trapezoid Area via Rotation
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2015-01-12 19:32
PolygonTransformationGeometric ConstructionSlider Animation
① This GeoGebra example dynamically demonstrates the derivation of the trapezoid area formula by rotating the trapezoid 180 degrees to form a parallelogram, visually showing why area equals (base1 + base2) × height / 2. ② Core math concepts include trapezoid area, geometric transformations (rotation and symmetry), polygon area, and properties of perpendicular lines and segments. ③ Construction highlights: using commands such as Segment, Line, Point, OrthogonalLine, Intersect, Polygon, Midpoint, and Rotate; objects include vertices A, B, C, D, E, F, the original polygon poly1, its rotated copy poly1', and corresponding sides a, b, c, d and their rotated versions a', b', c', d'; a Slider controls the rotation angle for interactive exploration. ④ Suitable for middle school geometry classes to help students understand the area formula, explore invariance of area under rigid transformations, and develop spatial reasoning and logical thinking.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Line(C, a) → b
  3. Point(b) → D
  4. Segment(C, D) → c
  5. OrthogonalLine(C, a) → f
  6. Intersect(f, a) → E
  7. Segment(E, C) → h
  8. Polygon(A, C, D, B) → poly1, a_1, c_1, d, b_1
  9. Midpoint(d) → F
  10. Rotate(A, Slider, F) → A'
  11. Rotate(C, Slider, F) → C'
  12. Rotate(D, Slider, F) → D'
  13. Rotate(B, Slider, F) → B'
  14. Polygon(A', C', D', B') → poly1', a', c', d', b'

AI Drawing Prompt Reference

Draw a trapezoid and its rotated parallelogram. The trapezoid is formed by points A, B, C, and D, where A and B are the endpoints of the base, and C and D are the endpoints of the top. The height is a perpendicular line segment. The parallelogram is the trapezoid rotated 180 degrees to form. The vertices of the parallelogram are the rotated copies of the trapezoid's vertices. Show the area formula ( (base1 + base2) × height / 2 ). Use a slider to control the rotation angle for interactive exploration. The drawing should clearly display the trapezoid, parallelogram, bases, height, and rotation relationships.
The prompt above was compiled from the original drawing commands and is for reference only.