in euclidean plane geometry, a quadrilateral is a polygon with four edges (or sides) and four vertices (or corners). sometimes, the term quadrangle is used (similar to the term "triangle"), while other times, the term tetragon is used (similar to pentagon, 5-sided polygon, and hexagon, 6-sided polygon). a quadrilateral with vertices formula_1, formula_2, formula_3, formula_4 is sometimes written as formula_5.