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Triangle Area Proof

Triangle Area Proof
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2014-10-03 19:47
TriangleCoordinate GeometryGeometric Construction
This example dynamically demonstrates the proof that the area of a triangle is half the base times the height. It starts with triangle ABC, constructs orthogonal lines, intersections, and segments to mark the base and height, and calculates the area. Key math concepts include triangle area formula, orthogonal projection, and vectors. GeoGebra commands used are Polygon, OrthogonalLine, Intersect, Segment, etc., making it suitable for high school geometry teaching and construction learning.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. OrthogonalLine(A, a) → e
  3. Intersect(a, e) → D
  4. Segment(D, A) → h
  5. Angle(A, D, B) → α
  6. Angle(h, a) → β
  7. Angle(poly1) → γ, δ, ε
  8. Polygon(A, D, B) → poly2, b_1, m, d
  9. Polygon(A, D, C) → poly3, c_1, n, d_1

AI Drawing Prompt Reference

Draw a triangle and dynamically demonstrate that its area is half the base times the height. Start by drawing the triangle, then construct perpendicular lines from the vertices to the opposite sides to mark the base and height. Use the perpendicular lines and intersection points to create auxiliary shapes and calculate the area. Highlight key geometric concepts like orthogonal projection and vectors, suitable for high school geometry teaching and construction learning.
The prompt above was compiled from the original drawing commands and is for reference only.