Minimize Perimeter: Dynamic Optimization with Similar Triangles

① This example demonstrates how to minimize the perimeter of a triangle under given constraints using dynamic geometry, revealing the geometric meaning of optimization. ② Core mathematical concepts include similar triangles, perimeter calculation, functional relationships, power functions, and differential equations (for describing extremum conditions), bridging geometric constraints and algebraic modeling. ③ Construction highlights: Using GeoGebra commands such as Point, Segment, Midpoint, Angle, and AngularBisector, the construction builds multiple similar triangles with objects A, B, C, D, E, F, G, H, and parameters a, b, c, etc. The perimeter is computed in real time and displayed via text objects text1 to text6, while sliders or parameters allow dynamic variation to observe the function graph of perimeter versus variables. ④ Suitable for high school to early college students, this example helps understand geometric extrema, function optimization, and the role of differential equations in geometric problems, and can serve as material for mathematical modeling or inquiry-based learning.