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Proportional Division by Parallel Lines in a Triangle

Proportional Division by Parallel Lines in a Triangle
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2014-11-24 18:06
TriangleFunctionGeometric Construction
This example demonstrates the proportional division of a triangle's sides by parallel lines. It involves core mathematical concepts like the basic proportionality theorem (Thales' theorem) and similar triangles. The construction uses GeoGebra commands and objects such as Polygon, Point, Line, Intersect, Distance, Segment, Midpoint, and Corner. It is suitable for high school geometry instruction to visually illustrate and verify the theorem.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Point(poly1) → D
  3. Line(D, b) → d
  4. Intersect(d, a) → E
  5. Distance(A, D) → distanceAD
  6. Distance(D, B) → distanceDB
  7. Distance(C, E) → distanceCE
  8. Distance(E, B) → distanceEB
  9. Segment(D, E) → e
  10. Midpoint(b) → F
  11. Midpoint(e) → G
  12. Corner(1, 1) → Cnr1
  13. Corner(1, 2) → Cnr2
  14. Corner(1, 3) → Cnr3
  15. Corner(1, 4) → Cnr4
  16. Polygon(CN1, CN2, CN3, CN4) → Panel, cn1, cn2, cn3, cn4