Perpendicular Line Through an External Point: Compass-and-Ruler Construction

This example demonstrates how to construct a perpendicular line to a given straight line through a point P that lies outside the line. It uses a classic compass-and-ruler strategy with dynamic visualization to show the construction workflow with and without GeoGebra. The key mathematics includes perpendicularity, circle-based constructions, distance equality (same radius), and the use of circle–line/circle–circle intersections to identify points that enforce the required angle relationships. In GeoGebra, the build relies on commands such as Point, PointIn, Distance, Circle, Line, and Intersect, producing construction points (e.g., A, B, E) from circle intersections and then forming the candidate perpendicular line via Line. The activity is supported by interactive elements (step/animation controls and on-screen instructions) to guide students through each step and verify the result. Suitable for middle and high school geometry lessons, drill on geometric constructions, and learning interactive geometry with GeoGebra.