Orientador: Prof. Dr. Márcio Fabiano da Silva / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Mestrado Profissional em Matemática em Rede Nacional - PROFMAT, 2014. / Baseados no artigo de M. Josefsson, zemos nossos estudos dos quadriláteros convexos, mais precisamente dos trapézios, e buscamos por fundamentações que os caracterizassem. Estudamos seus ângulos, seus lados, as medidas de suas áreas e estabelecemos relações entre seus elementos, lançando mão de diversos teoremas, como o Postulado de Pasch, mas nossa principal fundamentação está no Postulado das Paralelas. / Based on the paper of M. Josefsson we have elaborated our studies on the convex quadrilaterals, more precisely the trapezoids, and searched for fundamentations which would characterize them. We have studied their angles, their sides, their areas and stabilished relations to their elements, making use of several theorems as the Pasch's Postulate, however, our main fundamentation is on the Parallel Postulate.

Title: The Collection of Exercises About Qaudrangles Author: Bc. Pavel Nohál Department: Department of Mathematics Education Supervisor: doc. RNDr. Jarmila Robová, CSc., Department of Mathematics Education Abstract: The master thesis is focused on exercises regarding qaudrangles. This gives a chance to pupils of primary schools and lower secondary schools to repeat and practice math curriculum with a view of further study, but also develop pupils' common sense and logical thinking. The quadrangles are being encountered by us every day and therefore the exercises in this area are largely connected with the practical life. As not many current Collections on the market are dealing exclusively with quadrangles, author would like to fill this vacancy by this thesis. Keywords: Quadrilaterals and their division Parallelograms and trapezoids Circumference and area Tops, sides and interior angles