Ramona CLINCIU                                                                                
                                                                                                                                   
                                      TEACHING BASICS OF THE DESCRIPTIVE GEOMETRY – RELATIVE POSITIONS 
                                                                                                                                   
                                                                                                                                   
                                                                                                       OF LINES AND PLANES 
                                                                                                                                   
                                                                                                                                   
                                             Abstract: The paper presents applications developed for teaching descriptive geometry. The purpose of the 
                                             applications is represented by the understanding of the basic elements of the descriptive geometry – the 
                                             lines  and  the  planes  and  their  relative  positions  in  space.  The  applications  are  focused  on  the  line 
                                             contained in a plane, this item being very important for the other relative positions of a line and a plane – 
                                             the line concurrent with a plane and the line parallel to a plane. 
                                                                                                                                   
                                             Key words: Descriptive geometry, line, plane, trace of a line, trace of a plane, relative positions line-
                                             plane. 
                                                                                                                                   
                                              
                                  1. INTRODUCTION                                                                                          The relative positions of two straight lines are issues 
                                                                                                                                      that usually do not raise any problem of understanding, 
                                        The paper presents applications which may be used in                                          while teaching them.  
                                  teaching descriptive geometry, for the understanding of                                                  As  to  the  relative  positions  of  two  planes,  a  very 
                                  the relative positions of a line towards a plane. The main                                          important  problem  is  represented  by  the  intersecting 
                                  purpose  of  these  applications  is  represented  by  the                                          planes. Students are taught to intersect planes of different 
                                  development and improvement of the spatial ability of                                               types.  By  the  end  of  this  explanation,  they  should 
                                  the students such as to enable the understanding of the                                             connect the intersection of planes with the type of lines 
                                  basic elements of the descriptive geometry – the line and                                           located  in  the  planes  considered.  For  example,  a 
                                  the plane.                                                                                          horizontal line (N) is obtained by intersecting a plane of 
                                        Descriptive geometry is a subject taught in the first                                         general  position  [P]  with  a horizontal  plane  [N]. As  a 
                                  year  of  the  university  studies  and,  in  general,  the                                         consequence,  one  should  consider  placing  a  horizontal 
                                  knowledge of the students related to this subject is not                                            line (N) in a plane of general position [P] (Figure 6, a), 
                                  quite  satisfactory.  For  most  of  the  students,  the                                            with its vertical trace V on like trace of the plane (Pv), as 
                                  knowledge related to geometry in general reduces to the                                             well as in a horizontal plane [N] (Figure 6, b),  with its 
                                  elements taught in primary and secondary school, during                                             vertical trace V on like trace of the plane (Nv). As to the 
                                  the high school classes they do not study geometry at all.                                          horizontal line considered, (N), it might be possible that 
                                  This fact explains why it is very important for them to                                             no one or probably only a few students would consider 
                                  understand and to assimilate fast  the  principles  of  this                                        placing  it  in  a  horizontal  projecting  plane  [P]  ^  [H] 
                                  subject,  from  the  very  beginning.  As  a  consequence,                                          (Figure 6, c). 
                                  teachers need to find methods that would provide support                                                 The paper presents applications which are focused on 
                                  for  the  students  to  understand  easily  the  problems                                           the relative positions of a line and a plane and especially 
                                  presented, they use different books, didactical materials,                                          on the problem of the line contained in a plane. The line 
                                  posters.  Also,  teachers  use  frequently  computers  and                                          contained in a plane is used in solving both the problem 
                                  video projectors, trying to find methods that would make                                            of  intersecting  a  line  with  a  plane,  and  in  solving  the 
                                  explanations  more  attractive  and  will  enable  the                                              problem of a line parallel to a plane. 
                                  understanding of the problems presented, increasing the                                                  The  applications  presented  in  this  paper  come  to 
                                  interest of the students in the taught subject.                                                     complete  other  applications  developed  for  teaching 
                                        The  study  of  the  descriptive  geometry  starts  with                                      problems of descriptive geometry [3], [4] and