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Area of a Triangle by Chelsea Gibbons

Area of a Triangle by Chelsea Gibbons
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2020-05-06 02:16
TriangleCoordinate Geometry
In collections The Area of a Triangle
This example demonstrates how to calculate the area of a triangle using geometric construction methods. Key mathematical concepts include the properties of triangles and area formulas. Using GeoGebra commands such as Segment, LineBisector, Point, Polygon, etc., the triangle can be dynamically constructed and its area observed. Suitable for middle school and above students to learn geometry and area calculation.

GeoGebra Commands & Parameters

  1. Segment(A, B) → AB
  2. LineBisector(AB) → b
  3. Point(b) → D
  4. Point(b) → C
  5. Segment(D, C) → CD
  6. OrthogonalLine(A, CD) → g
  7. Segment(C, A) → c
  8. Segment(D, A) → d
  9. Intersect(b, g) → E
  10. Polygon(C, E, A) → poly1, a_1, c_1, e_1
  11. Polygon(A, E, D) → poly3, d_4, a_2, e_3
  12. Midpoint(C, A) → F
  13. Midpoint(A, D) → H
  14. Rotate(A, rotateΔ, H) → A'
  15. Rotate(E, rotateΔ, H) → E'
  16. Rotate(D, rotateΔ, H) → D'
  17. Polygon(A', E', D') → poly3', d', a', e'
  18. Rotate(C, rotateΔ, F) → C'
  19. Rotate(E, rotateΔ, F) → E'_1
  20. Rotate(A, rotateΔ, F) → A'_1
  21. Polygon(C', E'_1, A'_1) → poly1', a'_1, c', e'_1
  22. Midpoint(A, E) → J
  23. Midpoint(D, C) → K
  24. Angle(C, E, A) → α
  25. Segment(A, E) → a
  26. Segment(C, E) → i
  27. Segment(D, E) → j
  28. Polygon(D, C, A) → poly5, a_3, d_5, c_3
  29. Midpoint(D, E) → G

AI Drawing Prompt Reference

Draw a triangle ABC and calculate its area using geometric construction methods. Start by drawing segment AB, then construct the perpendicular bisector b of AB and take points D and C on b. Draw segment CD, construct the perpendicular line g to AE, and draw segments AE and AD. Find the intersection point E of b and g, then use points A, E, and C to construct one triangle, and points A, E, and D to construct another. Next, construct points F and H, rotate the triangles to get new ones, and finally calculate the area of the triangle.
The prompt above was compiled from the original drawing commands and is for reference only.