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master's thesis
Dva svojstva simetrala kutova trokuta i Steiner-Lehmusov teorem
Zagreb: University of Zagreb, Faculty of Science, 2018. urn:nbn:hr:217:225279
Prosenečki, Ana
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Prosenečki, A. (2018). Dva svojstva simetrala kutova trokuta i Steiner-Lehmusov teorem (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:225279

Prosenečki, Ana. "Dva svojstva simetrala kutova trokuta i Steiner-Lehmusov teorem." Master's thesis, University of Zagreb, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:217:225279

Prosenečki, Ana. "Dva svojstva simetrala kutova trokuta i Steiner-Lehmusov teorem." Master's thesis, University of Zagreb, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:217:225279

Prosenečki, A. (2018). 'Dva svojstva simetrala kutova trokuta i Steiner-Lehmusov teorem', Master's thesis, University of Zagreb, Faculty of Science, accessed 26 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:225279

Prosenečki A. Dva svojstva simetrala kutova trokuta i Steiner-Lehmusov teorem [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2018 [cited 2024 November 26] Available at: https://urn.nsk.hr/urn:nbn:hr:217:225279

A. Prosenečki, "Dva svojstva simetrala kutova trokuta i Steiner-Lehmusov teorem", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2018. Available at: https://urn.nsk.hr/urn:nbn:hr:217:225279

Metadata
TitleDva svojstva simetrala kutova trokuta i Steiner-Lehmusov teorem
AuthorAna Prosenečki
MentorMario Krnić (mentor)
Committee memberMario Krnić (predsjednik povjerenstva)
Committee memberMea Bombardelli (član povjerenstva)
Committee memberGoran Radunović (član povjerenstva)
Committee memberZvonko Iljazović (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2018-11-27, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Cilj ovog diplomskog rada je izučavanje nekih značajnih svojstava simetrala kutova trokuta. Rad se sastoji od četiri poglavlja. Nakon uvodnog poglavlja, u drugom poglavlju bavimo se teoremom o simetrali kuta u trokutu. Dajemo nekoliko dokaza tog teorema kao i njegove inačice. Kao primjenu, dobivamo eksplicitne formule za duljine simetrala kutova trokuta. Nadalje, u istom poglavlju izvodimo nekoliko zanimljivih nejednakosti koje uključuju simetrale kutova trokuta. U trećem poglavlju dajemo nekoliko primjena jednostavne činjenice da simetrala kuta trokuta raspolavlja odgovarajući luk opisane kružnice trokuta. Nadalje, primjenom glavnih rezultata iz drugog i trećeg poglavlja rješavamo neke složenije geometrijske probleme s brojnih matematičkih natjecanja za srednjoškolce. Konačno, u četvrtom poglavlju dajemo nekoliko dokaza Steiner - Lehmusovog teorema koji kaže da ako trokut ima dvije simetrale kutova jednakih duljina, onda je on jednakokračan.
Abstract (english)
In the present thesis, we study some interesting properties of angle bisectors in a triangle. The thesis is divided into four chapters as follows: after an introductory chapter, in Chapter 2 we give several variants and proofs of an angle bisector theorem. As an application, we derive formulas for lenghts of angle bisectors of a triangle. Further, we also study some inequalities involving angle bisectors of a triangle. In Chapter 3 we utilize a simple fact that an angle bisector of a triangle bisects the corresponding arc of a circumscribed circle. As an application of main results from Chapters 2 and 3, we also solve some geometry problems appearing on numerous mathematical competitions for high school students. Finally, in Chapter 4 we give several proofs of the Steiner - Lehmus theorem which asserts that if the triangle has two equal angle bisectors, then it is isosceles.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:225279
Study programmeTitle: Mathematics Education; specializations in: Mathematics Education
Course: Mathematics Education
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-06-12 12:05:26