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Pythagoras' Theorem Proof with Similar Triangles

Pythagoras' Theorem Proof with Similar Triangles
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2016-02-01 03:58
TriangleTrigonometryGeometric Construction
This example proves Pythagoras' Theorem using similar triangles and lengths rather than areas. It closely follows the original idea of Pythagoras' Theorem. It uses Polygon, Line, Circle, Intersect, Angle, OrthogonalLine, Segment commands in GeoGebra to construct multiple triangles and segments. Suitable for middle school and above students to learn geometric proofs.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Polygon(D, F, E) → poly2, e, d, f
  3. Line(E, e) → g
  4. Circle(E, a^(2)) → h
  5. Intersect(h, g, 2) → G
  6. Polygon(E, F, G) → poly3, i, j, l
  7. Circle(E, b^(2)) → k
  8. Intersect(k, g, 1) → H
  9. Polygon(E, H, D) → poly4, d_1, e_2, h_1
  10. Angle(poly1) → α, β, γ
  11. Angle(poly2) → δ, ε, ζ
  12. Angle(poly4) → η, θ, ι
  13. Angle(poly3) → κ, λ, μ
  14. OrthogonalLine(D, e) → m
  15. Intersect(m, g) → I
  16. Segment(D, I) → n
  17. Segment(H, I) → p
  18. OrthogonalLine(F, e) → q
  19. Intersect(q, g) → J
  20. Segment(F, J) → r
  21. Segment(J, G) → s

AI Drawing Prompt Reference

Draw a right triangle with a hypotenuse. Construct a similar triangle outward on the hypotenuse. Drop a perpendicular from the right angle to the hypotenuse, dividing it into two segments. On each segment, construct a smaller right triangle similar to the original. Connect the foot of the perpendicular to points on the hypotenuse to form additional similar triangles. Label all interior angles of the triangles. Draw perpendiculars from the other vertices to the hypotenuse to show proportional relationships among the similar triangles.
The prompt above was compiled from the original drawing commands and is for reference only.