Dilation Preserves Angles: Dynamic Verification

This GeoGebra example dynamically demonstrates that dilation (a similarity transformation) preserves angle measures. The core mathematical concept is that dilation scales all distances by a constant factor from a center, but does not alter the shape, so corresponding angles remain equal. The construction uses the Polygon command to create an original triangle ABC, the Dilate command to generate dilated triangles (e.g., A'B'C') with respect to a center and scale factor, and the Angle command to measure corresponding angles α, β, γ. By dragging sliders or points, students can observe that the angle values remain unchanged. Additional commands such as Vector, Translate, and Midpoint are used for auxiliary constructions, and multiple dilated copies (poly1', poly1'_1) are included for comparison. This resource is suitable for middle school to high school students learning about similarity and transformations, and serves as an interactive visual proof in geometry instruction.