Final answer:
The statement is true; two-dimensional figures are congruent if they can be matched by translations, rotations, or reflections, as these transformations preserve the figures' shapes and sizes.
Step-by-step explanation:
The statement is true: Two-dimensional figures are congruent to each other if they can be obtained by either translations, rotations, or reflections. Congruent figures have the same size and shape but may be oriented differently in space. To be congruent, one figure can be moved (via translation), rotated, or flipped (reflected) to coincide exactly with the second figure.
Translations involve sliding the figure in any direction without changing its orientation or size. Rotations involve turning the figure around a fixed point at a certain angle. Reflections are like placing a figure over a mirror line which creates a mirror image of the original figure.
These three transformations preserve the size and shape of geometric figures, hence making them congruent. Each transformation has applications in real-world scenarios and forms the basis for many geometric proofs and problems.