4.4. Symmetries with GeoGebra
Choose any line r in the plane; this exercise works on symmetry with respect to the line r.
a) Draw a non-convex heptagon that stays within one of the half-planes defined by the line and use the “axial symmetry” tool to find the symmetric polygon of the drawn heptagon with respect to r, then analyze if the result makes sense to you.
b) We are going to verify that the definition of “symmetry” discussed in class holds. To do this, choose any vertex of the heptagon (let's call it C) and use the “Perpendicular” and “Compass” tools to find C' following the steps discussed in class:
- Draw the line s, which is perpendicular to r and passes through C (using the “Perpendicular” tool).
- Select the point where r and s intersect, let's call it D.
- Use the “Compass” tool to find another point on s that is equidistant from r, just like C. This point is C'.