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Triangle Area Problem

Triangle Area Problem
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2020-09-21 21:12
TriangleCoordinate GeometryGeometric Construction
This example demonstrates how to determine the area of a triangle based on the positions of points in the coordinate system. Key mathematical concepts include coordinate geometry and triangle area calculation. It uses commands such as PointIn, Polygon, Segment, SurdText, Mode, Length, If, and Intersect in GeoGebra. Suitable for middle school and above students to learn triangle area calculation and coordinate geometry.

GeoGebra Commands & Parameters

  1. PointIn(e) → A
  2. PointIn(l(x, y) ∧ x ≥ x(A)) → C
  3. PointIn(j) → B
  4. Polygon(A, C, B) → t1, b_1, a_1, c_1
  5. Segment(A, B) → f
  6. Segment(B, C) → g
  7. Segment(C, A) → h
  8. SurdText(f) → text1
  9. SurdText(g) → text2
  10. SurdText(h) → text3
  11. SurdText(t1) → text4
  12. Mode(l1) → l2
  13. Length(l2) → i
  14. If(i ≟ 0, "No coordinates repeat!", "You have repeated coordinates.") → text5
  15. Intersect(p, eq1) → D
  16. Intersect(eq1, q) → E
  17. Intersect(q, eq2) → F
  18. Intersect(eq2, r) → G
  19. Polygon(A, G, C) → t2, c_2, a_2, g_1
  20. Polygon(A, F, B) → t4, b_2, a_4, f_1
  21. Intersect(eq3, p) → H
  22. Polygon(B, H, A) → t5, a_5, b_3, h_1
  23. Polygon(B, E, C) → t6, c_4, b_4, e_1
  24. Intersect(r, eq3) → I
  25. Polygon(B, I, C) → t7, c_5, b_5, i_1

AI Drawing Prompt Reference

Draw a triangle formed by points A, B, and C. Connect A-B, B-C, and C-A to form segments f, g, and h, and label them with text. Calculate segment lengths and check for repeated coordinates. Use intersection points to construct multiple triangles, such as triangles t2, t4, t5, t6, and t7. Text labels include segments and triangles.
The prompt above was compiled from the original drawing commands and is for reference only.