1. komponenta

Lecture type	Total
Lectures	45
Exercises	30

* Load is given in academic hour (1 academic hour = 45 minutes)

COURSE AIMS AND OBJECTIVES: This is the introductory course in geometry at this study. The aim of the course is to systematize, consolidate and deepen the knowledge of elementary (high school, synthetic) plane geometry without too much encroachment into the axiomatic construction of geometry.

COURSE DESCRIPTION AND SYLLABUS:
Introduction: about axioms, basic definitions, angles, sum of angle measures in a triangle
Congruence of triangles: definition and theorems on congruence of triangles, properties of parallelograms and rhombuses
Relationship of sides and angles in a triangle, isosceles triangle, triangle inequality
Midsegment of a triangle, midsegment of a trapezoid
Circle: theorem on perimeter and central angle and basic consequences
Bisector of a line and bisector of an angle. Circumscribed, inscribed and escribed circles of a triangle
Geometric constructions: ruler and compass, four basic constructions of a triangle, four steps in solving construction problems (analysis, description of the construction, proof, discussion). Intersection method
Similarity of triangles: Thales' theorem on proportionality, definition and theorems on similarity of triangles
Perimeter and area: formulas for the area of a triangle and some quadrilaterals, Pythagoras' theorem, Heron's formula. Area method
Triangle geometry: Theorem on the bisector of an angle in a triangle. Orthocenter. Centroid. Euler's line. Cevin's and Menelaus' Theorem
Quadrilateral and Circle: Cyclic Quadrilateral (Characterization), Ptolemy's Theorem, Tangential Quadrilateral (Characterization)

1. Elementarna geometrija, skripta, D. Ilišević, M. Bombardelli.
2. Elementarna matematika 1, B. Pavković, D. Veljan, Školska knjiga, Zagreb, 2004.
3. Geometrijske konstrukcije, D. Palman, Element, Zagreb, 1996.

Mandatory course - Regular study - Mathematics Education