4.2. Dynamic Geometry with GeoGebra
We say that a construction is well done with GeoGebra when the properties that characterize the construction are maintained, even when we drag (pull on the vertices) the figures with the pointer.
Practice creating well-made constructions with simple elements:
a) Line parallel to a segment. Draw a segment and a line parallel to it that passes through a point not on the segment. If you draw the parallel line by eye, when you modify the segment, the line will no longer be parallel to it.
To create the parallel line correctly, use the “Segment between two points” tool and the “Parallel line” tool. Once you do this, drag one of the ends of the segment with the pointer. What happens to the line?
b) Right triangle. Draw a right triangle by eye using the “Segment between two points” tool three times, or using the “Polygon” tool. Then, drag one of its vertices with the pointer and observe that the triangle is no longer a right triangle.
Repeat the construction in such a way that the triangle you have built is always a right triangle. To do this, you must use the “Perpendicular line” tool, then use the “Polygon” tool and click on the ends of the segment and on a point on the perpendicular line. Now drag one of the ends of the segment. What happens now with the triangle? Does it stop being a right triangle?
Hide the perpendicular line so that only the triangle remains (use the button “Show/Hide Object”).
c) Find the appropriate tools to construct a regular polygon and the perpendicular bisector of a segment so that they remain correctly constructed.