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Proof Without Words by Steve Phelps (7)

Proof Without Words by Steve Phelps (7)
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2015-02-03 22:16
TriangleCircleTrigonometryGeometric ConstructionSlider Animation
In collections Similarity & Right Triangle Trigonometry Similarity, Right Triangles, and Trigonometry (SRT) Cluster Proofs Without Words Proofs Without Words
This example demonstrates the Pythagorean Theorem through an interactive geometric proof by dragging points and a slider. It involves concepts like right triangles, equilateral triangles, unit circles, and quadrilaterals. Constructed using GeoGebra commands such as Point, Mirror, CircleArc, Polygon, Segment, OrthogonalLine, Dilate, Intersect, and Rotate. Ideal for high school mathematics education to visually understand the proof of the Pythagorean Theorem.

GeoGebra Commands & Parameters

  1. If(o ≤ 1, o, 1) → scalefactor
  2. Point(yAxis) → B
  3. Point(xAxis) → A
  4. Mirror(A, B) → A'
  5. CircleArc(B, C, A) → c
  6. Point(c) → D
  7. Polygon(D, A', 4) → poly1, e, f, g, h, E, F
  8. Segment(A, D) → a
  9. Segment(D, A') → b
  10. Segment(A, A') → d
  11. Polygon(A', A, 4) → poly2, i, j, k, l, G, H
  12. Polygon(A, D, 4) → poly3, m, n, p, q, I, J
  13. OrthogonalLine(D, i) → r
  14. Dilate(F, 1 - scalefactor, A) → F'
  15. Polygon(F', A', E) → poly4, b_1, c_1, d_1
  16. Intersect(r, k) → M
  17. Segment(D, M) → a_1
  18. If(1 < o ≤ 2, o - 1, 1) → rotatefactor
  19. Rotate(F', ((rotatefactor * 90))°, A') → F''
  20. Rotate(A', ((rotatefactor * 90))°, A') → A''
  21. Rotate(E, ((rotatefactor * 90))°, A') → E'
  22. Polygon(F'', A'', E') → poly4', e', f'', a''
  23. Intersect(i, a_1) → K
  24. If(o > 2, 3 - o, 1) → scalefactor2
  25. Dilate(D, scalefactor2, K) → D'
  26. Polygon(D', A', H) → poly5, h_1, d', a'
  27. Dilate(I, 1 - scalefactor, A') → I'
  28. Polygon(J, I', A) → poly6, a_2, j_1, i'
  29. Rotate(J, (-(((rotatefactor * 90))°)), A) → J'
  30. Rotate(I', (-(((rotatefactor * 90))°)), A) → I''
  31. Rotate(A, (-(((rotatefactor * 90))°)), A) → A'_1
  32. Polygon(J', I'', A'_1) → poly6', a'_1, j', i''
  33. Polygon(A, D', G) → poly7, g_1, a_3, d'_1