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Pythagorean Theorem Demonstration by Mathguru

Pythagorean Theorem Demonstration by Mathguru
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2012-05-30 14:36
TriangleAngleGeometric Construction
This example demonstrates the relationship in a right-angled triangle where the sum of the squares of the two legs equals the square of the hypotenuse. Core concepts include the Pythagorean Theorem, right-angled triangles, and side length calculations. Construction involves commands like Segment, Rotate, Angle, Line, and Intersect, with objects such as points A, B, a, α, B', β_1, β, A', γ, b, c, C, d, e. Suitable for middle school and above students to learn and apply the Pythagorean Theorem.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Rotate(B, α, A) → B'
  3. Angle(B, A, B') → β_1
  4. Rotate(A, -β, B) → A'
  5. Angle(A', B, A) → γ
  6. Line(A, B') → b
  7. Line(B, A') → c
  8. Intersect(b, c) → C
  9. Segment(C, A) → d
  10. Segment(C, B) → e

AI Drawing Prompt Reference

Draw a right triangle ABC with A as the right angle. First, draw side AB, then rotate point B to get point B', and draw lines AB' and BA'. Their intersection is point C. Finally, draw sides AC and BC.
The prompt above was compiled from the original drawing commands and is for reference only.