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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
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

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.
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[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.

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