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Triangle Area via Rectangle

Triangle Area via Rectangle
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2015-12-19 01:24
TriangleCoordinate GeometryTransformation
This example demonstrates the relationship between the area of a triangle and a rectangle inscribed within it, visually illustrating the derivation of the triangle area formula. Key math concepts include triangle area, rectangle area, geometric transformations, and coordinate geometry. GeoGebra commands and objects used in construction are Polygon, If, Rotate, Translate, and OrthogonalLine. Suitable for high school mathematics education to help students understand the derivation of the triangle area formula and enhance spatial reasoning skills.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → triangle, c, a, b
  2. If(a^(2) > b^(2) + c^(2), OrthogonalLine[A, a], If[b^(2) > a^(2) + c^(2), OrthogonalLine[B, b], OrthogonalLine[C, c]]) → d
  3. If(a^(2) > b^(2) + c^(2), Intersect[d, a], If[b^(2) > a^(2) + c^(2), Intersect[d, b], Intersect[d, c]]) → D
  4. If(a^(2) > b^(2) + c^(2), Polygon[A, D, C], If[b^(2) > a^(2) + c^(2), Polygon[B, C, D], Polygon[C, A, D]]) → triangle_1
  5. If(a^(2) > b^(2) + c^(2), Polygon[A, D, B], If[b^(2) > a^(2) + c^(2), Polygon[B, A, D], Polygon[C, B, D]]) → triangle_2
  6. Rotate(triangle_1, α, C) → poly1
  7. If(b^(2) > a^(2) + c^(2), Vector[C, B], Vector[C, A]) → u
  8. Translate(poly1, Vector[(u * n)]) → poly1'
  9. Rotate(triangle_2, α, B) → poly2
  10. If(a^(2) > b^(2) + c^(2), Vector[B, A], Vector[If[b^(2) > a^(2) + c^(2), Vector[B, A], Vector[B, C]]]) → v
  11. Translate(poly2, Vector[(v * n)]) → poly2'
  12. OrthogonalLine(B, b) → e
  13. If(a^(2) > b^(2) + c^(2), Segment[A, D], If[b^(2) > a^(2) + c^(2), Segment[B, D], Segment[C, D]]) → f