Difference-based Trigonometric Construction with Tangent Geometry

This example uses a “sum by difference” (Suma por diferencia) geometric relationship to connect difference-structured quantities with tangent geometry, illustrating how direction information can be realized as constructed tangent-related points and segments in a unified diagram. It centers on trigonometry (tangent), the geometric meaning of tangents, and vector-based direction handling, supported by standard construction transforms. In GeoGebra, the construction relies on Rotate, Vector, Polygon, Translate, and Mirror, together with many transformed (primed/double-primed) objects to show correspondences after each transformation. Key named points (e.g., A, B, C, D, F, G, I, P and intermediate points like H, E) and tangent/related objects (e.g., T1, T2, T3, T, plus quantities such as h_1, b_1, c_1, i_1) are arranged so the reader can visually track how the “difference-driven” setup affects the tangent geometry. Suitable for high school to early university learners for building geometric intuition about trigonometric tangents and for learning constructive visualization techniques.