Proof of the Relationship Between Two Perpendicular Lines

This GeoGebra example provides an interactive visual proof that the product of the slopes of two perpendicular lines equals -1. It demonstrates the fundamental algebraic condition for perpendicularity in the coordinate plane. Core mathematical concepts include linear functions, slope, perpendicularity criteria, and angle measurement. The construction uses commands such as Line to define lines f and g, OrthogonalLine to create perpendicular lines, Intersect to find their intersection point, and Angle to mark the right angle α. Points A, B, C, etc., serve as dynamic control points, while Segment connects relevant points. Text objects (tekst1, tekst3, etc.) dynamically display the slopes rc_1 and rc_2 and their product, reinforcing the proof. This resource is suitable for middle school (grades 8-9) or high school students learning coordinate geometry, and can be used for self-exploration or teacher-led demonstrations to bridge geometric intuition and algebraic proof.