Volume 4, Issue 5, October 2018, Page: 40-44
Modification Cross’ Theorem on Triangle with Congruence
M. Rusdi Syawaludin, Department of Mathematics, University of Riau, Pekanbaru, Indonesia
Mashadi Mashadi, Department of Mathematics, University of Riau, Pekanbaru, Indonesia
Sri Gemawati, Department of Mathematics, University of Riau, Pekanbaru, Indonesia
Received: Dec. 29, 2018;       Accepted: Jan. 15, 2019;       Published: Feb. 18, 2019
DOI: 10.11648/j.ijtam.20180405.11      View  107      Downloads  31
Abstract
Cross’ theorem states if any triangle ABC, on each side constructed a square and vertices of the square are connected, it will form another triangle which has an equal area to triangle ABC. In this paper we will discuss the modification Cross’ theorem on triangle, which is to construct a square outcase direction on each side triangle produced by Cross’ theorem. The purpose of this paper is to modify Cross’ theorem and give simple proof even junior or senior high school can answer. The process of proof is done in simple way, that is using a congruence approach. The result obtained are square vertices that are connected is form a trapezoid and have area 5 times the area of triangle ABC.
Keywords
Triangle, Square, Congruence, Cross’ Theorem
To cite this article
M. Rusdi Syawaludin, Mashadi Mashadi, Sri Gemawati, Modification Cross’ Theorem on Triangle with Congruence, International Journal of Theoretical and Applied Mathematics. Vol. 4, No. 5, 2018, pp. 40-44. doi: 10.11648/j.ijtam.20180405.11
Copyright
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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