Question

helena was curious if quadrilaterals qrst and x yzw were congruent, so she tried to map one figure onto the other using transformations: helena concluded: \its not possible to map qrst onto x yzw using a sequence of rigid transformations, so the quadrilaterals are not congruent.\ what error did helena make in her conclusion?

Explanation:

Rigid transformations (translations, rotations, reflections) preserve congruence. Helena likely missed that a rotation (or other rigid transformation) could map QRST to X Y Z W. Congruent figures can be mapped via rigid transformations, so her error was not considering all rigid transformation sequences (like rotation) to check congruence.

Answer:

Helena failed to consider that a rotation (along with other rigid transformations) could be part of the sequence to map QRST onto X Y Z W; rigid transformations preserve congruence, so not testing all rigid transformation sequences (including rotation) to check congruence was her error.