Vukoja, Marijana
(2014)
*Visine trokuta i konstruktivni problemi.*
Diploma thesis, Faculty of Science > Department of Mathematics.

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## Abstract

At the beginning of this thesis basic concepts are defined, such as the height of the triangle and the orthocentre. Some properties of the orthocentre are listed and proven. In this work we demonstrate that the lines in which the heights lie are Ceva lines. The Euler line and the Feuerbach circle are also described. The second chapter is devoted to constructive problems. It is also described what a constructive task should include and what it can be. Next we focus to the construction of a triangle in which at least one given element is height. There are 47 such triangle structures. 36 of them are solvable, 10 structures are not solvable and one has not got a solution. The first few examples have all necessary steps a constructive task has to contain; other examples have only a detailed analysis.

Item Type: | Thesis (Diploma thesis) |
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Supervisor: | Varošanec, Sanja |

Date: | 2014 |

Number of Pages: | 52 |

Subjects: | NATURAL SCIENCES > Mathematics |

Divisions: | Faculty of Science > Department of Mathematics |

Depositing User: | Iva Prah |

Date Deposited: | 01 Sep 2015 13:03 |

Last Modified: | 01 Sep 2015 13:03 |

URI: | http://digre.pmf.unizg.hr/id/eprint/4208 |

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