Question

Consider triangles abc and triangles def, not shown based on the definition of congruence, in terms of rigid motions which statments are invalid

Answer 1

Any statement suggesting that congruent triangles cannot be mapped onto each other using rigid motions or that non-rigid transformations can result in congruent triangles is invalid.

Step-by-step explanation:

In the context of congruent triangles, rigid motions refer to moves that do not alter the shape or size of a figure, such as rotations, reflections, translations, and combinations of these. If triangles ABC and triangles DEF are congruent, they can be mapped onto each other using a sequence of these rigid motions. Any statement that implies that triangles can be congruent without being able to be mapped onto each other using rigid motions is invalid. This is because congruence in geometry is defined as having the exact same size and shape, and rigid motions are the only transformations that maintain both. Therefore, any statement suggesting that a non-rigid transformation (which alters size or shape) can result in congruent triangles would be incorrect.