Dilation-Based Splitting of Triangle Sides (Geo.3.5 Lesson 1)

This example demonstrates how to split the sides of a triangle using a dilation (scaling) approach, making the division points correspond to a prescribed geometric ratio. The key math concepts include dilation/similarity transformations, proportional division of line segments, and the geometric interpretation of piecewise or parameter-driven relationships; it is also framed around circle geometry such as the circumcircle/circumscribed circle connections. Construction highlights: the provided GeoGebra summary shows the use of Polygon to create the triangle-related objects D, E, and F, together with points t1, d, f, and e that represent the key division/intermediate construction points. Their placement and updating are driven by the underlying ratio/parameter logic, enabling a clear visualization of how the triangle’s sides are partitioned. Suitable for advanced secondary geometry, contest preparation, and GeoGebra instruction on similarity and transformation-based constructions.