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Pythagoras' Theorem Proof 1

Pythagoras' Theorem Proof 1
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2014-05-30 17:21
TrigonometryCoordinate GeometryGeometric Construction
In collections Pythagoras' Theorem
This example provides a visual demonstration of the proof of Pythagoras' Theorem. It involves core mathematical concepts such as Pythagorean Theorem, Differential Calculus, and Geometric Construction. The construction utilizes commands like Polygon, OrthogonalLine, and Intersect. It is suitable for high school students learning about the proof of Pythagoras' Theorem.

GeoGebra Commands & Parameters

  1. Polygon(B, A, 4) → poly1, b, c, d, e, D, E
  2. Polygon(C, B, 4) → poly2, f, g, h, i, F, G
  3. Polygon(A, C, B) → poly3, b_1, a_1, c_1
  4. OrthogonalLine(B, b_1) → j
  5. Polygon(A, C, 4) → poly4, k, l, m, n, H, I
  6. Intersect(j, m) → J
  7. Intersect(j, b_1) → K
  8. Polygon(I, J, K, A) → poly5, i_1, j_1, k_1, a_2
  9. Polygon(J, H, C, K) → poly6, j_2, h_1, c_2, k_2
  10. Polygon(A, B, C) → poly7, c_3, a_3, b_2

AI Drawing Prompt Reference

Draw three squares with the sides of a right triangle as their edges. Inside the squares on the longer legs, use geometric constructions such as perpendicular lines, intersection points, and connecting lines to visually demonstrate the proof of the Pythagorean theorem, forming multiple smaller triangles and quadrilaterals that illustrate the theorem's geometric meaning.
The prompt above was compiled from the original drawing commands and is for reference only.