Drawing vs. Constructing, The Drag Test
- Author:
- Dr. Jack L. Jackson II
Drawing vs. Constructing
In the app above there appear to be four congruent equilateral triangles. However, everything is not as it seems.
Select some points and drag them around to see what types of figures are actually here. Answer the questions posed above.
There is a difference in a geometric object that is merely drawn to temporarily have a certain shape, vs. a geometric object that is constructed with certain structure built in.
If the task is to construct an isosceles triangle, then the construction should stay an isosceles triangle when the figure is manipulated by dragging around the points. The structure of an isosceles triangle should remain as the figure is manipulated. If a figure can be manipulated to be a non-isosceles triangle, or even a non-triangle, then not enough structure was built into the construction. On the other hand, the figure should be able to be manipulated so that any isosceles triangle may be formed by the figure after manipulation. For example, if the figure always stays an equilateral triangle, then it is always an isosceles triangle, but it is not a general isosceles triangle, because there are some isosceles triangles that it cannot be manipulated to become.
Be sure when you are constructing objects that they have been constructed with enough structure maintain the desired structure when manipulated, and that they do not have too much structure built in, so that they can be manipulated to become any example of the desired object.
The main power of GeoGebra is in the construction of dynamic figures that stand up to the drag test.