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Title: Orthogonal projection onto the xy-plane for secondary schools Author: Martina Magová Department: Department of Mathematics Education Supervisor: RNDr. Vlasta Moravcová, Ph.D., Department of Mathematics Education Abstract: This thesis follows on from the bachelor thesis Position examples in an orthogonal projection onto the xy-plane with metric examples and analysis of the current state of teaching the orthogonal projection onto the xy-plane at secondary schools. It includes a variety of examples and exercises. For some of those, step-by-step constructions are available in the addendum. They have been adapted for projection using a dataprojector. The theoretical part including step-by-step constructions was also made available to the public via a webpage. The thesis is designed for secondary school students as a material for self study and as a tool for teachers, who can use the included examples and project the step-by-step constructions in class. Keywords: orthogonal projection, construction examples, position examples, metric examples

Author: Martina Magová Department: Department of Mathematics Education Supervisor: RNDr. Vlasta Moravcová, Ph.D., Department of Mathematics Education Abstract: This paper describes how to determine the relative position of two lines, a line and a plane or two planes in an orthogonal projection onto the xy-plane. It includes a variety of examples and exercises. For many of those, step-by-step constructions are available in the addendum, which have been adapted for projection using a dataprojector. The addendum also includes models for some examples, which are intended to be cut and assembled, that can help the reader vividly visualize the spatial situation. The paper is designed for secondary school students as a material for self study and as a tool for teachers, who can use the included examples and project the step-by-step constructions in class. Keywords: orthogonal projection, construction examples, position examples