TY - JOUR T1 - On the Thales Theorem in the Iso-Taxicab Plane AU - Akça, Ziya AU - Nazlı, Selahattin PY - 2023 DA - June JF - Hagia Sophia Journal of Geometry JO - HSJG PB - Salim YÜCE WT - DergiPark SN - 2687-4261 SP - 15 EP - 20 VL - 5 IS - 1 LA - en AB - There are non-Euclidean geometries that are both accessible in a very concrete form and close to Euclidean geometry in their basic structure. In this paper, we study the Iso-taxicab analogues of the intercept theorem, also known as Thales's theorem is an important theorem in elementary geometry. KW - The plane $\mathbb{R}_{\pi 3}^{2}$ KW - Thales theorem KW - non-Euclidean geometry CR - Akça, Z., Bayar, A., & Ekmekçi, S. (2007). The norm in CC-plane geometry. Pi Mu Epsilon Journal, 12(6), 321-324. CR - Bayar, A., Ekmekçi, S., & Z. Akça (2008). On the plane geometry with generalized absolute value metric. Mathematical problems in Engineering, 1-8. CR - Bayar, A., Ekmekçi, S., & Özcan, M. (2009). On trigonometric functions and cosine and sine rules in taxicab plane. International Electronic Journal of Geometry, 2(1), 17-24. CR - Bayar, A., Ekmekçi, S., & Öztürk, ̇I. (2015). On complex numbers and Taxicab plane. Mathematical Sciences and Applications E-Notes, 3(1), 58-64. CR - Çolakoğlu, H.B., & Kaya, R. (2008). Taxicab versions of the Pythagorean theorem. Pi Mu Epsilon Journal, 12(9), 535-539. CR - Ekmekçi, S., Akça, Z., & Altıntaş K. (2015). On trigonometric functions and norm in the generalized taxicab metric. Mathematical Sciences And Applications E-Notes, 3(2), 27-33. CR - Özcan, M., Ekmekçi, S., & Bayar, A. (2002). A note on the variation of the taxicab lengths under rotations. Pi Mu Epsilon Journal, 11(7), 381-384. CR - Sowell, K. O. (1989). Taxicab geometry—a new slant. Mathematics Magazine, 62(4), 238-248. CR - Kocayusufoğlu, İ. (2000). Trigonometry on Iso-taxicab geometry. Mathematical and Computational Applications, 5(3), 201-212. CR - Bayar, A., & Kaya, R. (2011). On isometries of $\mathbb{R}_{\pi n}^{2}.$. Hacettepe Journal of Mathematics and Statistics, 40(5), 673-679. CR - Akça, Z., & Nazlı, S. (2022). On the versions in the plane $\mathbb{R}_{\pi3}^{2}$ of some Euclidean theorems. New Trends in Mathematical Sciences, 10(1), 20-27. CR - Nazlı, S., & Akça, Z. (2020). On the trigonometric functions in $\mathbb{R}_{\pi 3}^{2}$. Konuralp Journal of Mathematics, 8(2), 429-437. CR - Akça, Z., & Nazlı, S. (2022). On the shortest distance of a point to the line in the plane $\mathbb{R}_{\pi 3}^{2}$. New Trends in Mathematical Sciences, 10(4), 128-132. UR - https://dergipark.org.tr/tr/pub/hsjg/issue//1259789 L1 - https://dergipark.org.tr/tr/download/article-file/2988081 ER -