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Dynamic Proof of Trapezoid Area Formula

Dynamic Proof of Trapezoid Area Formula
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2015-03-04 23:32
TrianglePolygonGeometric Construction
This example dynamically demonstrates the formula for the area of a trapezoid by dividing it into two triangles. It involves core mathematical concepts such as trapezoids, triangles, similar triangles, and the median value theorem. The construction uses GeoGebra commands like Vector, Line, Point, Polygon, OrthogonalLine, Intersect, and Segment. Suitable for middle school and above, it helps students understand the geometric basis and dynamic changes of the trapezoid area formula.

GeoGebra Commands & Parameters

  1. Vector(J, K) → u
  2. Line(A, B) → a
  3. Line(C, a) → b
  4. Point(a) → D
  5. Point(a) → E
  6. Point(b) → G
  7. Point(C, u) → F
  8. Polygon(D, E, G, F) → mnohoúhelník1, d, e, g, f
  9. OrthogonalLine(D, b) → c
  10. OrthogonalLine(G, a) → h
  11. Intersect(b, c) → H
  12. Intersect(h, a) → I
  13. Segment(D, H) → i
  14. Segment(G, I) → k
  15. Polygon(D, G, F) → mnohoúhelník2, f_1, d_1, g_1
  16. Polygon(D, E, G) → mnohoúhelník3, g_2, d_2, e_1
  17. Polygon(D, E, G, F) → mnohoúhelník4, d_3, e_2, g_3, f_2

AI Drawing Prompt Reference

Draw a trapezoid and divide it into two triangles to demonstrate the area formula. Start by drawing the two parallel sides of the trapezoid, then draw a perpendicular line from one vertex of the top side to the bottom side, marking the intersection point. Construct a triangle using this perpendicular line and the top side. Next, construct another triangle using the same perpendicular line and the bottom side. Finally, combine these two triangles to show the area formula of the trapezoid.
The prompt above was compiled from the original drawing commands and is for reference only.