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The Converse of Pythagoras' Theorem

The Converse of Pythagoras' Theorem
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2013-03-24 22:08
TriangleTrigonometry
This example demonstrates that when Pythagoras' theorem applies, the angle opposite the longest side in a triangle is only 90 degrees. Key mathematical concepts include trigonometry. Construction highlights the use of Segment, Rotate, Angle, Ray, Point, Polygon commands in GeoGebra. Suitable for middle school and above students and teachers.

GeoGebra Commands & Parameters

  1. Segment(A_1, B) → a_2
  2. Rotate(B, α°, A_1) → B'
  3. Angle(B, A_1, B') → β
  4. Ray(A_1, B') → b_2
  5. Point(b_2) → C
  6. Polygon(A_1, C, B) → poly1, b, a, c
  7. Angle(A_1, C, B) → γ
  8. Angle(C, B, A_1) → δ
  9. Angle(B, A_1, C) → A

AI Drawing Prompt Reference

Draw a triangle ABC with A as the vertex and B and C as the endpoints of the base. First, draw line segment AB, then rotate point B around A by a specified angle to get point B', next draw ray AB', and take point C on the ray. Finally, measure the angles at A, B, and C.
The prompt above was compiled from the original drawing commands and is for reference only.