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.
| Published in | International Journal of Theoretical and Applied Mathematics (Volume 4, Issue 5) |
| DOI | 10.11648/j.ijtam.20180405.11 |
| Page(s) | 40-44 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2019. Published by Science Publishing Group |
Triangle, Square, Congruence, Cross’ Theorem
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APA Style
M. Rusdi Syawaludin, Mashadi Mashadi, Sri Gemawati. (2019). Modification Cross’ Theorem on Triangle with Congruence. International Journal of Theoretical and Applied Mathematics, 4(5), 40-44. https://doi.org/10.11648/j.ijtam.20180405.11
ACS Style
M. Rusdi Syawaludin; Mashadi Mashadi; Sri Gemawati. Modification Cross’ Theorem on Triangle with Congruence. Int. J. Theor. Appl. Math. 2019, 4(5), 40-44. doi: 10.11648/j.ijtam.20180405.11
AMA Style
M. Rusdi Syawaludin, Mashadi Mashadi, Sri Gemawati. Modification Cross’ Theorem on Triangle with Congruence. Int J Theor Appl Math. 2019;4(5):40-44. doi: 10.11648/j.ijtam.20180405.11
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Download@article{10.11648/j.ijtam.20180405.11,
author = {M. Rusdi Syawaludin and Mashadi Mashadi and Sri Gemawati},
title = {Modification Cross’ Theorem on Triangle with Congruence},
journal = {International Journal of Theoretical and Applied Mathematics},
volume = {4},
number = {5},
pages = {40-44},
doi = {10.11648/j.ijtam.20180405.11},
url = {https://doi.org/10.11648/j.ijtam.20180405.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20180405.11},
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.},
year = {2019}
}
TY - JOUR T1 - Modification Cross’ Theorem on Triangle with Congruence AU - M. Rusdi Syawaludin AU - Mashadi Mashadi AU - Sri Gemawati Y1 - 2019/02/18 PY - 2019 N1 - https://doi.org/10.11648/j.ijtam.20180405.11 DO - 10.11648/j.ijtam.20180405.11 T2 - International Journal of Theoretical and Applied Mathematics JF - International Journal of Theoretical and Applied Mathematics JO - International Journal of Theoretical and Applied Mathematics SP - 40 EP - 44 PB - Science Publishing Group SN - 2575-5080 UR - https://doi.org/10.11648/j.ijtam.20180405.11 AB - 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. VL - 4 IS - 5 ER -
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