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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 10 | Year 2020 | Article Id. IJMTT-V66I10P519 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I10P519

Alternative Proofs for the Length of Angle Bisectors Theorem on Triangle


Amelia, Mashadi, Sri Gemawati
Abstract

The purpose of the paper is to introduces alternative proofs for the length of Angle Bisectors Theorem on Triangle. In this paper the author proofs it with a simple way that uses law of sines, Pythagoras theorem, Ptolemy’s theorem, and similarity.

Keywords
Angle bisector, Ptolemy's theorem, similar triangles
References

[1] G.W.I.S. Amarasinghe, “On the standard lengths of angle bisectors and the angle bisector theorem”, Global Journal of Advanced Research on Classical and Modern Geometries, 1 (1) (2012), 15-27.
[2] Mashadi, Geometri (Edisi 2), Pusbangdik Universitas Riau, Pekanbaru, 2015.
[3] Mashadi, Geometri Lanjut, Pusbangdik Universitas Riau, Pekanbaru, 2015.
[4] Mashadi, Geometri Lanjut II, Pusbangdik Universitas Riau, Pekanbaru, 2020.
[5] Mashadi, S. Gemawati, Hasriati, dan H. Herlinawati, “Semi excircle of quadrilateral”, JP Journal of Mathematical Sciences, 15 (1 & 2) (2015), 1-13.
[6] Mashadi, Chitra Valentika, dan Sri Gemawati, “Development of Napoleon’s Theorem on the Rectangles in Case of Inside Direction”, International Journal of Theoretical and Applied Mathematics, 3 (2) (2017), 54-57.
[7] Mashadi, Chitra Valentika, Sri Gemawati, dan Hasriati, “The Development of Napoleon’s Theorem on the Quadrilateral in Case of Outside Direction”, Pure and Applied Mathematics Journal, 6 (4) (2017), 108-113.
[8] Ovidiu T. Pop dan Rodica D. Pop, “About the angle bisector in a triangle”, International Journal of Geometry, 2 (2) (2013), 83-86.
[9] G.W.I.S. Amarasinghe, “A concise elementary proof for the Ptolemy’s theorem”, Global Journal of Advanced Research on Classical and Modern Geometries, 2 (1) (2013), 20-25.
[10] D.N.V. Krishna, “The new proof of Ptolemy’s theorem & nine point circle theorem”, Mathematics and Computer Science, 1 (4) (2016), 93-100
[11] M. Miculita, “A new trigonometric proof to Ptolemy theorems in cyclic quadrilaterals”, International Journal of Geometry, 6 (2) (2017), 109-111.
[12] A. Scooper, “Length of Angle Bisector”, https://proofwiki.org/wiki/Length_of_Angle_Bisector, accessed December 10, 2019, at 8:50 p.m.
[13] P. Darmayasa, “Panjang Garis Bagi pada Segitiga dan Pembuktiannya”, https://www.konsep-matematika.com, accessed January 15, 2020, at 9.20 p.m.

Citation :

Amelia, Mashadi, Sri Gemawati, "Alternative Proofs for the Length of Angle Bisectors Theorem on Triangle," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 10, pp. 163-166, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I10P519

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