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Area Trisection: Equal Areas via Common Altitude

Area Trisection: Equal Areas via Common Altitude
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2014-10-27 06:31
TriangleGeometric Construction
In collections Dissecting a Triangle Into Three Equal Areas
This example demonstrates how dividing side BC into three equal parts allows splitting triangle ABC into three triangles of equal area. Since these triangles share the same altitude, their areas are equal, each being 1/3 of the original. Construction involves GeoGebra commands like Polygon, PointIn, and Dilate to create triangles and mark points. Suitable for middle school students learning geometric area concepts or for understanding altitude-based area relationships.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Dilate(B, 0.6666666666666666, C) → D
  3. Dilate(B, 0.3333333333333333, C) → E
  4. Polygon(A, B, D) → poly2, b', a_1, b_1
  5. Polygon(A, D, E) → poly3, b'_1, a_2, b'_2
  6. Polygon(A, E, C) → poly4, c_1, a_3, b'_3
  7. PointIn(poly2) → Pointpoly2
  8. PointIn(poly3) → Pointpoly3
  9. PointIn(poly4) → Pointpoly4

AI Drawing Prompt Reference

Draw a triangle with its base divided into three equal parts. Connect each division point to the opposite vertex to form three smaller triangles, demonstrating that they share the same altitude and thus have equal areas.
The prompt above was compiled from the original drawing commands and is for reference only.