CD Tesis

Eksistensi Segitiga Sama Sisi dan Kosiklik pada Trisektor Sudut Segitiga Siku-siku

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In any polygon, especially a triangle, several special lines can be given. One of them is the angle trisector. An angle trisector is two lines that divide an angle into three equal parts. One theorem that uses angle trisectors is Morley’s Theorem. Basically, Morley’s Theorem applies angle trisectors to the inner angles of any triangle. From these angle trisector lines, several intersection points are obtained, three of which can form an equilateral triangle. This equilateral triangle became known as the Morley
Triangle.
Various developments have been made to Morley’s Theorem. These developments are focused on the types of corner trisectors, namely inner angle trisectors, supplementary angle trisectors, and outer angle trisectors. By using a combination of the three types of angle trisectors which are then applied to all corners of any triangle, 27 equilateral triangles are produced.
By disregarding the angle trisector at one corner of any triangle, a problem will arise, that is an equilateral triangle cannot be formed except by providing three types of angle trisectors at the other two angles simultaneously.
To be able to produce an equilateral triangle by providing one type of angle trisector or a combination of two or even three types of angle trisectors at both corners of the triangle, the type of triangle needs to be modified to become a right triangle. Furthermore, by providing one and a combination of the three types of angle trisectors at non-right angles, 37 equilateral triangles are produced, consisting of 26 equilateral triangles without the cocyclic concept and 11 equilateral triangles using the cocyclic concept. There are also some of the resulting equilateral triangles that are equilateral triangles that cannot be found by applying Morley’s Theorem using any triangle. The sine rule and cocyclic theorem are used to prove that the resulting triangle is an equilateral triangle.
Keywords: Inner angle trisector, outer angle trisector, supplementary angle trisector, Morley’s Theorem, Morley’s Triangle

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Ketersediaan

Informasi Detail

Judul Seri

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No. Panggil

2010241834

Penerbit

Pekanbaru : Universitas Riau – Pascasarjana – Tesis Matematika., 2023

Deskripsi Fisik

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Bahasa

Indonesia

ISBN/ISSN

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Klasifikasi

2010241834

Tipe Isi

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Tipe Media

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Tipe Pembawa

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Edisi

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Subjek

MATEMATIKA

Info Detail Spesifik

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Pernyataan Tanggungjawab

Jaka

Versi lain/terkait

Lampiran Berkas

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