Parallel and Perpendicular Lines in Dynamic Construction

This example demonstrates how parallel and perpendicular constraints drive a connected geometric construction: key points and lines are determined in a coordinated way, with dynamic labels that help visualize the relationships. It centers on fundamental ideas such as parallel lines, perpendicular (normal) lines, representing line directions via slopes/parameters, and linking these constructions to circle-related objects (e.g., circumscribed/circumcircle components) and function-style elements (including quadratic-function connections). Construction-wise, the GeoGebra workflow relies on the commands “Line” and “perp”, with conditional logic via “If”. Objects A, B, C, D are used alongside line/parameter entities s₁, s₂ and m₁, m₂ to form and track the relevant lines; the use of infty supports direction handling for the perpendicular construction. Multiple text elements (text1–text4 and text5) and marker/annotation objects (parr) provide clear visual parameter feedback. Suitable for middle school through early university, especially for lessons on geometric construction, coordinate-geometry reasoning, and dynamic geometry visualization.