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Proof of Area of an Obtuse Triangle

Proof of Area of an Obtuse Triangle
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2015-04-28 13:36
TriangleTrigonometryGeometric Construction
In collections Area of Polygons
This example demonstrates the calculation and proof method for the area of an obtuse triangle. It involves core mathematical concepts such as trigonometry, geometric construction, and area formula derivation. The construction uses GeoGebra commands like Segment and Angle to draw the obtuse triangle and auxiliary lines, defining points, segments, angles, and text objects. It is suitable for high school mathematics teaching, helping students understand the derivation and application of the area formula for obtuse triangles.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Segment(B, C) → b
  3. Segment(C, A) → c
  4. Segment(A, D) → d
  5. Segment(D, B) → e
  6. Angle(B, D, A) → α

AI Drawing Prompt Reference

Draw an obtuse triangle ABC with points A, B, and C as its vertices. Construct auxiliary line segments AD and BD through point A, making angle BDA an obtuse angle. Draw the three sides of triangle ABC, a, b, and c, as well as the auxiliary line segments d and e.
The prompt above was compiled from the original drawing commands and is for reference only.