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Pythagorean Theorem Proof Using Similar Triangles

Pythagorean Theorem Proof Using Similar Triangles
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2013-10-19 17:16
TriangleAngleGeometric Construction
In collections Proofs Without Words
This example demonstrates the Pythagorean Theorem using similar triangles. It involves the concept of similar triangles. Using GeoGebra commands such as Midpoint, Circle, Point, Polygon, OrthogonalLine, Intersect, Segment, Angle, it constructs multiple triangles and shows their similarity. Suitable for middle school and above students to learn geometric proofs.

GeoGebra Commands & Parameters

  1. Midpoint(A, B) → O
  2. Circle(O, A) → c_2
  3. Point(c_2) → C
  4. Polygon(A, B, C) → polígono1, c, a, b
  5. OrthogonalLine(C, c) → e
  6. Intersect(e, c) → D
  7. Segment(A, D) → m
  8. Segment(D, B) → n
  9. Segment(D, C) → h
  10. Angle(B, A, C) → α
  11. Angle(D, C, B) → α_1
  12. Angle(C, B, A) → β
  13. Angle(A, C, B) → γ
  14. Angle(A, C, D) → β_1

AI Drawing Prompt Reference

Draw a right triangle ABC with point O as the midpoint of AB. Draw a circle with O as the center and OA as the radius, intersecting AB at point C. Connect AC and BC to form triangle ABC. Construct CD perpendicular to AB, intersecting the circle at D, and connect AD and BD to form a new triangle. Measure angles α, α₁, β, γ, and β₁ to demonstrate the similarity of triangles and prove the Pythagorean theorem.
The prompt above was compiled from the original drawing commands and is for reference only.