Proof: Area of a Triangle 2
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In collections
Proof of Sine Rule, Cosine Rule, Area of a Triangle
This GeoGebra example provides a geometric proof of the triangle area formula by constructing a triangle with given vertices and auxiliary elements. It demonstrates how the area formula arises from the relationship between base, height, and the triangle's shape. Core mathematical concepts include the triangle area formula, base-height relationship, and geometric decomposition. Construction uses GeoGebra commands such as Intersect, Point, Segment, Polygon, and Angle, with key objects including vertices A, B, C, height segment h, and related lines. The interactive model is suitable for middle and high school mathematics, helping students visualize and understand the derivation of the triangle area formula through dynamic geometry.
GeoGebra Commands & Parameters
Intersect(xAxis, yAxis) → BPoint(xAxis) → CSegment(A, B) → cSegment(B, C) → aSegment(C, A) → bSegment(A, X) → hSegment(A, X) → fSegment(A, C) → gPolygon(A, X, C) → t1, c_1, a_1, x_1Polygon(A, B, C) → t2, c_2, a_2, b_1Angle(A, X, B) → α