Cutting a rectangle into two congruent triangles

This task shows the congruence of two triangles in a particular geometric context arising by cutting a rectangle in half along the diagonal. The teacher may wish to have students think about part (d) of the problem first before going through parts (a) through (c). The grid has been added to the background as a geometric aid and as a means of determining lengths of sides. For part (d), the grid may need to be extended depending on which translations, rotations, and reflections the students choose to use.