# CALQUES 2

Calques Géométriques allows the user to create any Euclidian construction (i.e. any construction which can be constructed with a compass and a straight-edge). The problem diagram is drawn in a menu-driven environment. The student chooses a tool and indicates points, line-segments or circles by using a mouse (for instance: he chooses point at midpoint and clicks on the two endpoints of a line-segment, then Chypre constructs the midpoint of the segment). The diagram can be started again with new points as basic objects. This interface is similar to many dynamic geometry softwares like Cabri Géomètre or The Geometer's Sketchpad Calques Géométriques is widely used by French teachers. It is used in a way similar to the Geometric Supposer with the aid of Calques, students construct a problem diagram and explore the problem to generate conjectures and to verify some properties. Students usually work in pairs in a computer laboratory, guided by a worksheet prepared by the teacher. In another way, Calques is commonly used by teachers for proof-reading. The screen of a computer is projected overhead and Calques is used as a super blackboard. The teacher explains proofs to the whole class, using visual justifications. For instance, the following exercise is a non-obvious problem given in a senior secondary school.

Let C1, C2, C3 be three circles with same radius and respective centers a, b, c. K is a point common to the three circles. The circles intersect by pair on A, B, C. Proof that K is intersection point of the altitudes of ABC.

Figure : A visual proof as it appears in Calques Géométriques. Sheet #1: terms of the problem. Sheet #2: from circles to rhombuses. Sheet #3: from rhombuses to a parallelogram. Sheet #4: prove that AK and ab are perpendicular.

This problem is difficult because a complete diagram becomes very unmanageable. With Calques, the diagram could be separated into several diagrams and the sequence of these diagrams may be considered as an obvious visual proof . A pencil is also available with which the teacher can mark some signs on the diagram. Nevertheless, Calques doesn’t contain expert knowledge for problem-solving. It was necessary to add a specific component dedicated to proof-constructions.

Calques includes many other features. See the examples (animated GIF).