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Investigation of Triangle Sides and Angles

Investigation of Triangle Sides and Angles
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2013-08-03 20:54
TriangleAngleGeometric Construction
In collections Properties of Polygons
This example investigates the relationship between the squares of the sides and angles in right, acute, and obtuse triangles. It demonstrates the mathematical connection between the lengths of the sides and the angles of a triangle. The construction uses commands such as Point, Segment, Rotate, Ray, Circle, Intersect, Polygon, and Angle, suitable for middle school and above students for geometric construction and exploration.

GeoGebra Commands & Parameters

  1. Point(Circle[A, a]) → B
  2. Segment(A, B) → c
  3. Rotate(A, α, B) → A'
  4. Ray(B, A') → d
  5. Circle(B, b) → e
  6. Intersect(e, d, 1) → C
  7. Polygon(A, B, C) → poly1, c_1, a_1, b_1
  8. Polygon(A, B, 4) → poly2, a_2, b_2, f, g, D, E
  9. Polygon(B, C, 4) → poly3, b_3, c_2, h, i, F, G
  10. Polygon(C, A, 4) → poly4, c_3, a_3, j, k, H, I
  11. Angle(poly1) → β, γ, δ
  12. If(l ≟ 1, b^(2), "?") → B5
  13. If(l ≟ 1, b_1^(2), "?") → C5
  14. If(l ≟ 1, a^(2), "?") → A5
  15. If(l ≟ 1, If[A9 > C5, ">", If[A9 ≟ C5, "=", "<"]], "?") → B9
  16. If(l ≟ 1, If[A9 > C5, ">", If[A9 ≟ C5, "=", "<"]], "?") → B8
  17. If(l ≟ 1, C5, "?") → C9

AI Drawing Prompt Reference

Draw a right triangle, then a acute triangle and an obtuse triangle. Mark the three sides and three angles in each triangle. Calculate the square of each side and compare it with the corresponding angle.
The prompt above was compiled from the original drawing commands and is for reference only.