When a figure can be shifted, turned, or flipped and still remain congruent, this is a sign of what?

When a figure can be shifted, turned, or flipped and still remain congruent, it clearly demonstrates the concept of congruence. Congruent figures are those that have the same shape and size, meaning that one figure can be transformed into another through movements such as translations, rotations, or reflections. These transformations do not alter the dimensions or angles of the figures involved; hence, congruence is preserved.

In the context of this question, congruence is distinguished from similarity, which involves figures that have the same shape but may differ in size. Equivalent figures, while could be interpreted in various contexts, generally refer to figures that have equal area but might not share congruence. Homothetic figures relate to figures that maintain the same shape and orientation through scaling transformations, but do not necessarily imply direct congruence. Thus, the essence of being able to manipulate a figure through these motions while maintaining its size and shape signifies that the figures are congruent.