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Mashadi Mashadi
Pusat Teknologi Bahan Industri Nuklir – BATAN Gedung 71-BATAN Kawasan Puspiptek Serpong, Tangerang Selatan 15314
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Alternative Proofs for the Side Trisector Lengths Theorem of a Triangle Rahmayani, Indah; Mashadi, Mashadi; Gemawati, Sri
Jurnal Matematika Integratif Vol 22, No 1: April 2026
Publisher : Department of Matematics, Universitas Padjadjaran

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24198/jmi.v22.n1.70223.91-100

Abstract

In general, discussions regarding the line for side trisectors are still relatively limited compared to angle trisectors. For angle trisectors, most studies only discuss Morley’s Theorem and its extensions. Meanwhile, for side trisectors, existing papers usually calculate the lengths using both the sides and the angles of the triangle. A common problem is how to find the side trisectors length from its opposite vertex when only the side lengths are known. Furthermore, if the side trisector line is extended to form a tangential excircle, can we determine its radius. In this article, we discuss several alternative proofs to determine the lengths produced by side trisectors in a triangle. The main focus is to derive a formula for the side trisectors length using only the original side lengths and to find the radius of the tangential excircle. These proofs are done simply by using several geometric approaches, such as trigonometry, Stewart’s Theorem, and the Pythagorean Theorem. The result provide a standard formula for the trisector length, which is then used to find the radius of the tangential excircle in the constructed triangle
Alternative Proof of the Butterfly Theorem on a Hyperbola Teguh, M.; Mashadi, Mashadi
Jurnal Matematika Integratif Vol 22, No 1: April 2026
Publisher : Department of Matematics, Universitas Padjadjaran

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24198/jmi.v22.n1.70222.73-82

Abstract

The Butterfly Theorem originally applies to a circle. Several researchers have proven the Butterfly Theorem using various methods of proof. Furthermore, the theorem has been extended from its original application on circles to other conic sections, namely the parabola and the ellipse, also through different proof techniques. In addition, the development of the Butterfly Theorem can be applied to another conic section, the hyperbola, through an analytic approach. In this paper, the author proves the Butterfly Theorem on a hyperbola using Haruki’s Lemma. Haruki’s Lemma was originally established for circles. Therefore, the author develops Haruki’s Lemma specifically for the hyperbola, which is then used to prove the Butterfly Theorem on a hyperbola. Thus, a new proof of the Butterfly Theorem on a hyperbola can be established
Peningkatan Aktivitas dan Hasil Belajar IPA Materi Tubuh Sehat melalui Metode Pembelajaran Jigsaw (Penelitian Tindakan Kelas Peserta Didik Kelas I Semester 1 SDN Ngiyono Tahun Pelajaran 2016/2017) Mashadi, Mashadi
JPI (Jurnal Pendidikan Indonesia): Jurnal Ilmiah Pendidikan Vol 4, No 1 (2018): JPI (Jurnal Pendidikan Indonesia): Jurnal Ilmiah Pendidikan
Publisher : Universitas Sebelas Maret

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20961/jpiuns.v5i1.33818

Abstract

Abstract. The purpose of this study was to improve the activities andlearning outcomes of science in class 1 students in the first semester on theHealthy Body material in Ngiyono Public Elementary School through theJigsaw learning method in the 2016/2017 school year. This type of researchis Classroom Action Research conducted in 2 cycles consisting of 2meetings with 4 stages each cycle, namely planning, implementing actions,observing, and reflecting. The research subjects were class I students,totaling 18 students. Data collection methods used are observation, tests,and documentation. The results of this study are an increase in the activitiesand learning outcomes of science students in class I. This is shown from thepre cycle average value of activities and student learning outcomes is 70.55by 7 students. In the first cycle the average value of activities and learningoutcomes of students is 78.80 by 11 students while in the second cycle theaverage value of the results of activities and student learning outcomes is86.67 by 16 students from 18 students. The activities and learning outcomesof students in science subjects in Healthy Body material in class I insemester 1 increased with the application of the Jigsaw learning method andhad fulfilled the indicator of success of 75%.
Co-Authors A, Finu Audian A. Mahendra, A. Aang Munawar Abdul Ghofur Adil Fadillah Ahmad, Cicin Akhmad Aminuddin Bama, Akhmad Aminuddin Alberta Rika Pratiwi Amwila P, Andi Yudha Andi Alatas, Andi Andriani, Dessy Astrini, Danti Audian A, Finu Ayu Puspita, Dian Badru, Mohamad Bambang Sugeng Barutu, Fabelia Andani Chatarina Umbul Wahyuni Chezy WM Vermila, Chezy WM Dafit Feriyanto Damar, Stenlly Dianta Ginting Dinata, Muhammad Farhan Eka Pratama, Berli Fionari, Gebi Fitrian, Achmad Gen Gen Gendalasari Gian Villany Golwa Gustia Kusuma Wardani Hadi, Nariman Hariadi Hariadi Hassanee, Narrong Heti Herawati Husnul Khatimah Hutabarat, Arnold Sultantio Hutajulu, Olnes Yosefa I Gusti Ayu Arwati Jamalludin, Jamalludin Jamaludin . Jaya, Pinto Kesambamula, Eldipalma Khim, Soei Khoir, Ahmad Din KHUZAIMAH Kinanti Wijaya, Kinanti Kusuma Wardani, Gustia Kusuma, Arya Diki Mahidin Mahidin Mahrani, Mahrani Mariana Mariana Marlina, Gusti Marniati, Felicitas Sri Melisasmi, Melisasmi Muhammad Rifqi muhammad rizky, muhammad Mumuh Mulyana Mustaqimah Mustaqimah Novita Sari Nurmaya Arofah Pratama, Berli Eka Pratiwi, Delisa Putri, Rika Andriyani Rachmawati, Indri Rahmayani, Indah Ramlan, H. Ratih Puspitasari Retno Martanti Endah Lestari Riyadi, Rizal Rusliana, Selvia Naca Saeful Yusuf Sapridawati, Yeni Sasmi, Meli Satyamulya, Reynaldi Rivanus Seprido Seprido, Seprido Setyo Purwanto SIREGAR, TESALONIKA Sitorus, Mido Ester Soedargo, Bayu Sri Gemawati Sugik Sugiantoro, Sugik Sukmana, Sugi Andrian Sulistiono susanto, haris Syafitri, sukma Novia Tambunan, Melenia Tarigan, Kontan Teguh, M. Tilopa, Era Napra Togar Saragi, Togar Vermila, Chezy Wibisono, Sandy Wisnu A. Adi Wisnu Ari Adi Yoyon Supriadi Yuliardani, Novita Yuliarty, Popi Yunasfi . yunasfi yunasfi Yunasfi, Yunasfi - Yusdira, Ade Zul Azhar