Similar Triangles with Multiplication Factor (Dynamic Demo)
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① This GeoGebra example dynamically demonstrates two similar triangles, where the second triangle is obtained by scaling the first by a fixed multiplication factor (scale ratio), visually showing the relationship between side lengths and angles in a similarity transformation. ② Core mathematical concepts include similar triangles, similarity ratio (multiplication factor), similarity transformation (homothety or scaling), and the properties that corresponding angles are equal and corresponding sides are proportional. ③ Construction highlights: uses Circle and Intersect commands to determine key points, Polygon to construct triangles, and Angle tool to mark corresponding angles; objects include A, F, B, K, c, d, C, D, E, t1, b, a, e, G, H, I, t2, h, g, i, multiple text labels (tekst1~tekst6) and Greek letters α, β, γ, δ for displaying side ratios and angle measures. ④ Suitable for middle school geometry or high school plane geometry review, useful for exploring the criteria and properties of similar triangles, and as a dynamic teaching aid to understand the effect of scaling transformations on figures.
GeoGebra Commands & Parameters
Circle(A, 7) → cCircle(B, 5) → dIntersect(c, d) → C, D, ,Polygon(A, E, B) → t1, b, a, ePolygon(G, I, H) → t2, h, g, iAngle(B, A, E) → αAngle(H, G, I) → βAngle(I, H, G) → γAngle(E, B, A) → δ