Exploration of Congruent Triangles
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) Show that there is a translation of the plane which maps A to D. Call B′ and C′ the images of B and C under this transformation. 2) Show that there is a rotation of the plane (by 304°) 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) Show that there is a reflection of the plane which does not move D or E and which maps C′′ to F. How do you find this line of reflection? 4) Print off your activity to turn in.