(斯坦纳——雷米欧斯定理Steiner-LehmusTheorem)如果一个三角形有两条内角平分线相等,则这个三角形为等腰三角形.已知:如图,△ABC中,BE平分∠ABC,CD平分∠ACB,BE=CD.求证:AB=AC. 答案 见解析解:若AB≠AC,不妨设AB>AC,∴∠ACB>∠ABC.∴∠DCB>∠EBC.∵BC=BC,BE=CD,∴BD=CE.作DH//BE且DH=BE,则EH=BD...
Steiner-Lehmus theoremequal bisectorsThe Steiner-Lehmus equal bisectors theorem originated in the mid 19th century. Despite its age, it would have been accessible to Euclid and his contemporaries. The theorem remains evergreen, with new proofs continuing to appear steadily. The theorem has fostered ...
We give a trigonometric proof of the Steiner-Lehmus Theorem in hyperbolic geometry. Precisely we show that if two internal bisectors of a triangle on the h... K Kiyota - 《Mathematics》 被引量: 3发表: 2015年 Steiner——Lehmus定理的代数证法 每个初学平面几何的学生都曾证明过这样一个十分简单的...
Mathematics - Metric GeometryWe give a trigonometric proof of the Steiner-Lehmus Theorem in hyperbolic geometry. Precisely we show that if two internal bisectors of a triangle on the hyperbolic plane are equal, then the triangle is isosceles.Keiji Kiyota...
M. Hajja, Other versions of the Steiner-Lehmus theorem, Amer. Math. Monthly, 108 (2001) 760-767.M. Hajja, Other versions of the Steiner-Lehmus theorem, Amer. Math. Monthly 108 (2001), 760-767.M. Hajja: Other versions of the Steiner-Lehmus theorem. Amer. Math. Monthly 108, 760-767...
a r X i v : 1 5 0 8 . 0 3 2 4 8 v 1 [ m a t h . M G ] 1 3 A u g 2 0 1 5 ATRIGONOMETRICPROOFOFTHESTEINER-LEHMUS THEOREMINHYPERBOLICGEOMETRY KEIJIKIYOTA Abstract.WegiveatrigonometricproofoftheSteiner-LehmusTheoremin hyperbolicgeometry.Preciselyweshowthatiftwointernalbisectorsofa ...
The Steiner-Lehmus Theorem has garnered much attention since its conception in the 1840s. A variety of proofs resulting from the posing of the theorem are still appearing today, well over 100 years later. There are some amazing similarities among these proofs, as different as they seem to be...
We prove that (i) a generalization of the Steiner-Lehmus theorem due to A. Henderson holds in Bachmann's standard ordered metric planes, (ii) that a variant of Steiner-Lehmus holds in all metric planes, and (iii) that the fact that a triangle with two congruent medians is isosceles ...
Negation-Free and Contradiction-Free Proof of the Steiner–Lehmus Theoremdoi:10.1215/00294527-2017-0019Victor PambuccianDuke University Press
A very short trigonometric proof of the Steiner-Lehmus theoremHAJJA, MOWAFFAQMitteilungen der Mathematischen Gesellschaft in Hamburg