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Proving Tri's Congruent (I)

Proving Tri's Congruent (I)
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2016-07-28 10:48
TriangleVectorGeometric Construction
In collections Prove Congruence through Transformations
This example demonstrates how to prove triangles congruent using transformational geometry. Core math concepts involved include symmetry, diagrams, limits, angles, and cuboids. GeoGebra commands and objects used in the construction are Polygon, Rotate, Vector, and Translate. Suitable for high school students learning geometric proofs and applications of transformational geometry.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Rotate(A, α, D) → A'
  3. Rotate(B, α, D) → B'
  4. Rotate(C, α, D) → C'
  5. Polygon(A', B', C') → poly1', c', a', b'
  6. Vector(E, F) → u
  7. Translate(A', u) → A''
  8. Translate(B', u) → B''
  9. Translate(C', u) → C''
  10. Polygon(A'', B'', C'') → poly1'', c'', a'', b''

AI Drawing Prompt Reference

Draw a triangle, then rotate it around a point to get a new triangle. Translate the new triangle using a vector, and translate it twice more to get two additional triangles. Finally, draw all four triangles in sequence to show the transformation relationships of rotation and translation.
The prompt above was compiled from the original drawing commands and is for reference only.