Thales' Theorem, Square Roots, and Similar Triangles

This example demonstrates the intrinsic relationship between Thales' theorem (a right angle inscribed in a semicircle) and similar triangles. By selecting points on a semicircle to construct right triangles, it uses properties of similar triangles to derive the geometric meaning of square roots. Core mathematical concepts include Thales' theorem, criteria and properties of similar triangles, Pythagorean theorem, and geometric representation of square roots. Construction details: Use Semicircle command to draw a semicircle, Point command to select points on it, Intersect command to find intersections, Segment command to draw line segments forming triangles, Angle command to measure angles, and Polygon command to generate polygons for similarity verification. Suitable for middle to high school mathematics teaching, can be used to explore right triangle properties, the relationship between similar ratios and square roots, or as a demonstration case for geometry construction teaching.