PERPENDICULAR_DISTANCE_THEORY.pdf

A novel side-length based determinant, the Perpendicular Distance Determinant (PDD), is introduced for the analysis of triangle geometry. This determinant enables a new classification of altitudes and the derivation of a unique area formula, providing insights into the fundamental properties of triangles. This work culminates in an axiom related to the determinacy of triangle dimensions, highlighting the foundational interdependence of side lengths and angles.