Congruence Of Convex Polygons
Main Article Content
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.
Downloads
Metrics
Article Details
You are free to:
- Share — copy and redistribute the material in any medium or format for any purpose, even commercially.
- Adapt — remix, transform, and build upon the material for any purpose, even commercially.
- The licensor cannot revoke these freedoms as long as you follow the license terms.
Under the following terms:
- Attribution — You must give appropriate credit , provide a link to the license, and indicate if changes were made . You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
Notices:
You do not have to comply with the license for elements of the material in the public domain or where your use is permitted by an applicable exception or limitation .
No warranties are given. The license may not give you all of the permissions necessary for your intended use. For example, other rights such as publicity, privacy, or moral rights may limit how you use the material.
