Everyday life in schools is an irrefutable witness of many students’ misinterpretations, as regards simple geometric concepts. For example, angle sizes, kinds of quadrilaterals and, even more significant, the heights of triangles are troubling the majority of students in primary and even in secondary schools, as we daily experience in classrooms.
So, a common “student slip”, as it is recorded in the relevant bibliography, is the observed difficulty in designing heights of triangles and, consequently, its intersection point (Orthocentre). Some students’ stereotypic - erroneous - perceptions, responsible for the mistaken construction of heights in triangles, are reported below:

• Triangles have one height
• Heights are vertical lines
• Orthocentre is placed inside the triangle, even in rectangular and obtuse triangles

Moreover, some students don’t mark the heights perpendicularly.
Certainly, confusion with respect to heights is perhaps intensified because of the polysemy, the different meaning that the mathematical language attributes in words of natural language. What we mean is the conflict between the geometric and the common meaning of the word “height”.
Taking all the above into account, we designed an activity within the context of tools of Cabri-Geometry II in order to support teaching the concept of height in triangles.
This interaction activity constitutes a microcosm within the digital geometry system of Cabri. Its operation is very simple and, thanks to user friendliness, the same user interface is kept. For this reason, this work thoroughly exploits the "type of button” software tool whereas, figures are also attractive to students, since their design is made using lots of colours.
Six types of learning activities are known to be performed using the tools of Cabri-Geometry II. One of them is constructions simulating real life problems. These activities can help students to develop strong motivation in their learning and approach mathematics as a human activity. Moreover, today, the prevailing theory of constructivism suggests that learning must take place within authentic situations, in a biomatic and collaborative way.
The proposed scenario, simulating a real-life problem is: “Three friends reside in 3 villages, somewhere in a flat area. The triangular region formed by the villages is encompassed by 3 motorways, which, per 2, pass through each village. It is essential that these 3 friends move along all the 3 motorways by bus every day.”

Some individual questions are:

• What is, firstly, the shortest path covered by each of the 3 friends so that they will go over to the opposite motorway?
• Will there be a common meeting point (perhaps a place of constructing a small hut) inside the formed triangular region for the 3 friends?
• What will be the arrangement of the vertices - the triangle’s villages - so that the 3 paths will always go through the same, internal point of the “triangular” region?
• Is there a special case in which the common meeting point is identified with one of the 3 villages?
• In all potential cases is there, always, a common meeting point?
• If we suppose that the 3 friends begin at the same time and move at the same speed, how will the vertices be positioned - villages of the triangle - so that the 3 friends (or 2) can meet at the same point?