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Pythagorean Theorem Proof Based on Similarity

Pythagorean Theorem Proof Based on Similarity
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2013-09-01 06:54
TriangleAngleGeometric Construction
In collections Pythagorean Theorem
This example demonstrates the Pythagorean theorem based on similarity. Using GeoGebra commands such as Segment, OrthogonalLine, and Rotate, it constructs the relationship between the sides of a triangle to illustrate the core concept of the theorem. Suitable for middle school and above students to learn geometric proofs.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. OrthogonalLine(A, a) → b
  3. Point(b) → C
  4. Segment(C, B) → c
  5. Segment(A, C) → d
  6. Rotate(C, 90*°, A) → C'
  7. OrthogonalLine(A, c) → e
  8. Intersect(e, c) → D
  9. Angle(C, D, A) → β
  10. Angle(C, B, A) → γ
  11. Segment(A, D) → f
  12. Angle(A, C, D) → ζ
  13. Angle(B, A, C) → α
  14. Angle(B, A, D) → δ
  15. Angle(D, A, C) → ε
  16. Polygon(B, A, C) → poly1, c_1, b_1, a_1

AI Drawing Prompt Reference

Draw a right triangle ABC with AB as the hypotenuse and BC and AC as the legs. Construct a perpendicular line from point C to AB, intersecting at point D. Then rotate point C to get point C', and draw angles β, γ, ζ, α, δ, and ε. Finally, draw quadrilateral BADC.
The prompt above was compiled from the original drawing commands and is for reference only.