Congruence Of Convex Polygons

Abstract

The study aimed to determine the conditions for the congruence of convex polygons by using direct proof, specifically the two-column proof under Euclidean geometry. Patterns of the existing postulates and theorems on triangles and convex quadrilaterals were discovered. Moreover, another proof of the theorems on the congruence of convex quadrilaterals were formulated by establishing Nth Angle Theorem. Furthermore, since the patterns on the congruence of triangles and convex quadrilaterals are perfectly correlated, conjectures were derived from these arrays. That is, two convex n-gons are congruent if and only if their corresponding: n-2 consecutive sides and n-1 angles are respectively congruent; n-1 sides and n-2 included angles are respectively congruent; and n sides and n-3 angles are respectively congruent. In addition, to verify the conjectures theorems on the congruence of convex pentagons and convex hexagons were proven. Since there is strong evidence that holds for the conjectures of the congruence of convex polygons, it opens portal for other researchers to exactly predict and prove the congruence of other convex n-gons, where n >6.