So all edges must be $\sqrt{2}$. Set up equations for $AD = BD = CD = \sqrt{2}$:

Mon, 04 May 2026 23:54:42 +0000

# All Edges Must Be $ \\sqrt{2} $: Setting Up a Coordinate Geometry Challenge In the elegant world of Euclidean geometry, the lengths of segments define shape, symmetry, and balance. A particularly intriguing challenge arises when every edge of a geometric figure is constrained to be $ \\sqrt{2} $, a length rich in simplicity and algebraic beauty. Here, we explore how to construct a figure—such as a tetrahedron or a triangle—where $ AD = BD = CD = \\sqrt{2} $, revealing the mathematical backbone that ensures all edges maintain this exact length. This article derives the essential equations that enforce $ AD = BD = CD = \\sqrt{2} $, laying the foundation for precise geometric modeling. Whether used in spatial reasoning, 3D modeling, or olympiad geometry, understanding these equations unlocks powerful problem-solving tools. ---