Modification Cross’ Theorem on Triangle with Congruence

M. Rusdi Syawaludin; Mashadi Mashadi; Sri Gemawati

doi:doi:10.11648/j.ijtam.20180405.11

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Modification Cross’ Theorem on Triangle with Congruence

M. Rusdi Syawaludin, Mashadi Mashadi, Sri Gemawati

Published in International Journal of Theoretical and Applied Mathematics (Volume 4, Issue 5)

Received: 29 December 2018 Accepted: 15 January 2019 Published: 18 February 2019

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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.

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), 2024. Published by Science Publishing Group

Keywords

Triangle, Square, Congruence, Cross’ Theorem

References

[1]	L. Baker and I. Harris, a Day to Remember Kath Cross. Mathematics Teaching, (2004), 189, 20-22.
[2]	G. Faux, Happy 21st Birthday Cockcroft 243 and All The Other Threes, Mathematics Teaching, (2004), 189, 10-12.
[3]	J. Gilbey, Responding to Geoff Fauxs Challenge, Mathematics Teaching, (2005), 190, 16.
[4]	Manuel and Luis, Students’ Development of Mathematical Practices Based on The Use of Computational Technologies, Center for Research and Advanced Studies, (2006).
[5]	Mashadi, Geometri Lanjut, UR Press, Pekanbaru, (2015).
[6]	Mashadi, Geometri: Edisi Kedua, UR Press, Pekanbaru, (2015).
[7]	Mashadi, Pengajaran Matematika, UR Press, Pekanbaru, (2015).
[8]	Mashadi, C. Valentika and S. Gemawati, Developtment of Napoleon on the Rectangles in Case of Inside Direction”, International Journal of Theoretical and Applied Mathematics, (2017), 3 (2), 54-57.
[9]	C. Valentika, Mashadi and S. Gemawati, The Development of Napoleons Theorem on The Quadrilateral in Case of Outside Direction, Pure and Applied Mathematics Journal, (2017), 108-113.
[10]	C. Valentika, Mashadi and S. Gemawati, the Development of Napoleons Theorem on Quadrilateral with Congruence and Trigonometry, Bulletin of Mathematics, (2017), 8 (01), 97-108.
[11]	Viliers, An Example of Discovery Function of Proof, Mathematics in School, (2017), 36 (4), 9-11.

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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

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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

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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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@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}
}

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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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Author Information

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

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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

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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

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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

Copy | 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}
}

Copy | Download

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  -

Copy | Download