Question

How do you connect the ideas of congruency and rigid motion and how do you prove congruency?

Answer 1

If you cut a triangle out of a piece of paper, and move that triangle around (sliding, rotating, reflecting) then that triangle will retain its original shape and size. The three movement types mentioned are rigid motions. They do not change the size or shape of the triangle. If two triangles are congruent, then a sequence of one or more rigid motions can be applied to have them line up together.