Constructing Similar Triangles via Symmetry and Angle Control

This example demonstrates how to construct similar triangles under given geometric constraints, using symmetry-related ideas and strict angle control to ensure corresponding sides are proportional and corresponding angles are equal. The key mathematics includes the similarity concept (e.g., angle-angle style reasoning), the scale-factor viewpoint behind similar transformations, and geometric construction logic that locates vertices via intersections. Construction workflow: Segment, Point, Line, and Ray set up the base elements and auxiliary rays; Intersect determines the critical vertex positions from the intersections; Angle is used to construct and verify target angles (such as α, β, γ, δ); Polygon then connects the computed points to form the final similar-triangle shape. The construction is organized around key points (A, B, C, D, E, F, G, H, etc.) and named lines/rays (f, g, h, i, m, n, etc.), with text labels (e.g., text1) to highlight the angle relations and construction steps. Suitable for middle/high school geometry lessons, contest preparation, and interactive demonstrations of “from conditions to construction” reasoning.