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Why Is the Area of a Triangle (b ∙ h)/2? Visual Proof

Why Is the Area of a Triangle (b ∙ h)/2? Visual Proof
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2012-12-09 17:30
TrianglePolygonGeometric Construction
In collections Euclidean Geometry
This example demonstrates the intuitive proof of the triangle area formula (b ∙ h)/2 by dissecting a triangle into a parallelogram with the same area. It uses Polygon, OrthogonalLine, Intersect, Segment, Midpoint, Rotate, etc., in GeoGebra. Suitable for middle school and above students learning geometry.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → t1, c, a, b
  2. OrthogonalLine(C, c) → f
  3. Intersect(f, c) → H
  4. Segment(C, H) → g
  5. Midpoint(A, B) → D
  6. Midpoint(B, C) → E
  7. Polygon(A, D, E, C) → q1, a_1, d, e, c_1
  8. Polygon(D, B, E) → t2, e_1, d_1, b_1
  9. Rotate(D, α, E) → D'
  10. Rotate(B, α, E) → B'
  11. Rotate(E, α, E) → E'
  12. Polygon(D', B', E') → t2', e', d', b'

AI Drawing Prompt Reference

Draw a triangle ABC, then dissect it into a parallelogram with the same area. First, draw triangle ABC, then draw a perpendicular line from C to AB and find the foot of the perpendicular H. Connect CH. Next, find the midpoints D and E of AB and BC, respectively, and draw triangle ADE and quadrilateral DEBC. Then, rotate quadrilateral DEBC around point E to overlap with triangle ABC, forming a new parallelogram.
The prompt above was compiled from the original drawing commands and is for reference only.