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Triangle to Rectangle Dissection

Triangle to Rectangle Dissection
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2017-01-10 11:41
VectorCoordinate GeometryGeometric Construction
This example demonstrates how to dissect a triangle into a rectangle. It involves core mathematical concepts such as coordinate geometry, vectors, transformations, and geometric construction. Key construction steps use GeoGebra commands like Polygon, Midpoint, Rotate, Line, OrthogonalLine, Intersect, Segment, Vector, and Translate. Suitable for high school mathematics students and teachers for teaching and exploring geometric transformations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Midpoint(c) → D
  3. Midpoint(a) → E
  4. Polygon(E, D, B) → poly2, b_1, e, d
  5. Rotate(E, (-α), E) → E'
  6. Rotate(D, (-α), E) → D'
  7. Rotate(B, (-α), E) → B'
  8. Polygon(E', D', B') → poly2', b', e', d'
  9. Line(A, C) → f
  10. OrthogonalLine(B, f) → g
  11. Intersect(f, g) → F
  12. Segment(B, F) → h
  13. Polygon(A, D, E, C) → poly3, a_1, d_1, e_1, c_1
  14. OrthogonalLine(D, f) → i
  15. Intersect(f, i) → G
  16. Polygon(A, D, G) → poly4, g_1, a_2, d_2
  17. Vector(A, (k, 0.38)) → u
  18. Translate(A, u) → A'
  19. Translate(D, u) → D'_1
  20. Translate(G, u) → G'
  21. Polygon(A', D'_1, G') → poly4', g', a', d'_1
  22. Polygon(D, E, C, G) → poly5, d_3, e_2, c_2, g_2

AI Drawing Prompt Reference

Draw a triangle ABC and dissect it into a rectangle. First, find the midpoints D and E of AB and AC respectively. Then, rotate D and B around E by -α degrees to get D' and B'. Draw a triangle with D', E', and B' as vertices. Next, draw a line f through A and C, and draw a perpendicular line g from B to f, finding their intersection F. Draw a line segment BF. Then, draw a quadrilateral with A, D, E, and C as vertices. Draw a perpendicular line i from D to f, finding their intersection G. Draw a triangle with A, D, and G as vertices. Next, move A 0.38 units along the positive x-axis to get A', move D and G 0.38 units along the same direction to get D'_1 and G', and draw a triangle with A', D'_1, and G' as vertices. Finally, draw a quadrilateral with D, E, C, and G as vertices.
The prompt above was compiled from the original drawing commands and is for reference only.