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Properties of the Ratio of Areas of Triangles

Properties of the Ratio of Areas of Triangles
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2018-04-21 01:09
TriangleGeometric Construction
This example demonstrates the properties of the ratio of areas of triangles. Key mathematical concepts include triangles, area ratios, and special points. Using GeoGebra commands such as Polygon, Segment, and OrthogonalLine, it illustrates how to understand the properties of area ratios through geometric construction. Suitable for middle school and above students.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → t1, c, a, b
  2. Segment(A, B) → f
  3. Segment(B, C) → g
  4. Segment(C, A) → h
  5. Segment(D, E) → i
  6. Segment(E, F) → j
  7. Segment(F, D) → k
  8. OrthogonalLine(A, a) → l
  9. Intersect(l, a) → G
  10. Segment(A, G) → m
  11. OrthogonalLine(D, j) → n
  12. Intersect(j, n) → H
  13. Segment(D, H) → p
  14. Polygon(D, E, F) → t2, f_1, d, e
  15. Segment(D, E) → q
  16. Segment(E, F) → r
  17. Segment(F, D) → s
  18. PointIn(t1) → Pointt1
  19. PointIn(t2) → Pointt2

AI Drawing Prompt Reference

Draw a triangle with labeled vertices. From two vertices, draw line segments to the third vertex to form the triangle. From one vertex, draw a perpendicular line to the opposite side, marking the intersection point. Repeat this from another vertex to create a second perpendicular line and mark its intersection. Connect these two intersection points with the third vertex to form a new triangle. Fill both triangles and indicate the ratio of their areas.
The prompt above was compiled from the original drawing commands and is for reference only.