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Inv 2.1 - Connecting Congruent Polygons

Inv 2.1 - Connecting Congruent Polygons
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2018-12-01 04:57
PolygonVectorTransformationGeometric Construction
This example demonstrates how to connect congruent polygons through rotation and translation operations. Core mathematical concepts include congruence, rotation, translation, and vectors. The construction utilizes GeoGebra commands and objects such as Intersect (intersection), Polygon (polygon), Rotate (rotation), Vector (vector), and Translate (translation). Suitable for high school students learning geometric transformations and vector concepts, helping to understand the principles and applications of shape transformations.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Polygon(A, B, C, D) → poly1, a, b, c, d
  3. Rotate(A, 85°, F) → A'
  4. Rotate(B, 85°, F) → B'
  5. Rotate(C, 85°, F) → C'
  6. Rotate(D, 85°, F) → D'
  7. Polygon(A', B', C', D') → poly1', a', b', c', d'
  8. Vector(D', E) → u
  9. Translate(E, u) → E'
  10. Vector(D', E) → v
  11. Translate(A', v) → R
  12. Translate(B', v) → S
  13. Translate(C', v) → P
  14. Translate(D', v) → Q
  15. Polygon(R, S, P, Q) → poly1'', a'', b'', c'', d''

AI Drawing Prompt Reference

Draw a square, then rotate it 85 degrees around a point to get another square. Use one vertex and the corresponding vertex of the new square to draw a line, and translate the other three vertices of the original square along this line to get four new points. Finally, draw a square with these four new points.
The prompt above was compiled from the original drawing commands and is for reference only.