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Proof Without Words: Pythagorean Theorem via Drag and Slider

Proof Without Words: Pythagorean Theorem via Drag and Slider
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2015-02-02 08:51
Coordinate GeometryGeometric 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 interactive dragging of points and a slider. It involves concepts like right triangles, Pythagorean theorem, geometric transformations, and coordinate geometry. Construction uses GeoGebra commands such as Point, Segment, Midpoint, Polygon, Mirror, Intersect, and Rotate. Suitable for middle or high school mathematics education to illustrate geometric proofs and coordinate geometry applications.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. Segment(A, B) → a
  4. Midpoint(a) → H
  5. Segment(A, H) → k
  6. Point(k) → C
  7. Polygon(C, B, 4) → poly1, b, c, d, e, D, E
  8. Polygon(A, C, 4) → poly2, f, g, h, i, F, G
  9. Mirror(C, H) → C'
  10. Polygon(A, G, C') → poly3, c', a_1, g_1
  11. Polygon(C', B, D) → poly4, d_1, c'_1, b_1
  12. Segment(E, C) → j
  13. Intersect(a_1, j) → I
  14. Rotate(C', (-α), D) → C''
  15. Rotate(B, (-α), D) → B'
  16. Rotate(D, (-α), D) → D'
  17. Polygon(C'', B', D') → poly4', d', c'', b'
  18. Rotate(A, α, G) → A'
  19. Rotate(G, α, G) → G'
  20. Rotate(C', α, G) → C''_1
  21. Polygon(A', G', C''_1) → poly3', c''_1, a', g'
  22. Polygon(G, C', D, E, F) → poly5, g_2, c'_2, d_2, e_1, f_1

AI Drawing Prompt Reference

Draw a horizontal segment on the x-axis with two endpoints. Mark its midpoint, then choose a point between the midpoint and the left endpoint. Construct two squares: one using the right endpoint and the chosen point, another using the chosen point and the left endpoint. Reflect the chosen point across the midpoint to get a symmetric point. Use this symmetric point and square vertices to form two right triangles, then rotate these triangles to fit around the squares. Finally, connect outer vertices to form a large square, visually demonstrating that the sum of the two smaller squares' areas equals the large square's area.
The prompt above was compiled from the original drawing commands and is for reference only.