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Ratios of Areas of Quadrilaterals

Ratios of Areas of Quadrilaterals
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2019-04-01 13:46
PolygonGeometric Construction
This example demonstrates the calculation and visualization of area ratios in quadrilaterals. Key math concepts include area of quadrilaterals, geometric distribution, geometric mean, and geometric transformations. It is constructed using GeoGebra commands like Polygon, LineBisector, Intersect, Segment, Circle, and PointIn. Suitable for high school mathematics education to understand geometric transformations and area relationships.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  2. LineBisector(D, A) → j
  3. LineBisector(D, C) → k
  4. Intersect(k, h) → F
  5. Intersect(j, g) → G
  6. Intersect(k, f) → H
  7. Intersect(j, i) → I
  8. Segment(F, H) → l
  9. Segment(I, G) → m
  10. Intersect(l, m) → E
  11. Circle(E, G) → c
  12. Segment(E, C) → n
  13. Segment(E, B) → p
  14. Segment(E, A) → q
  15. Segment(E, D) → r
  16. Intersect(c, r, 1) → J
  17. Intersect(c, n, 1) → K
  18. Intersect(c, p, 1) → L
  19. Intersect(c, q, 1) → M
  20. Polygon(J, K, L, M) → q1, j_1, k_1, l_1, m_1
  21. Intersect(m, m_1) → N
  22. Intersect(l, j_1) → O
  23. Intersect(m, k_1) → P
  24. Intersect(l, l_1) → Q
  25. PointIn(poly1) → Pointpoly1_1
  26. PointIn(q1) → Pointq1
  27. PointIn(poly1) → Pointpoly1