Exploration of Congruent Triangles
Use the tools in Geogebra to show that the two triangles ABC and DEF are congruent via the following steps, which produce a rigid transformation of the plane sending triangle ABC to triangle in DEF. 1. Create a translation of the plane which maps A to D. Call B′ and C′ the images of B and C under this transformation. 2. Create a rotation of the plane (by 304 degrees) which does not move D and which maps B′ to E. Call C′′ the image of C′ under this transformation. What point must we rotate the triangle about in order to achieve this? 3. Create a reflection of the plane which does not move D or E and which maps C′′ to F. How did you find this line of reflection?