Question

adam was curious if quadrilaterals abcd and gfeh were congruent, so he tried to map one figure onto the other using transformations.

image of grid with quadrilaterals gfeh (red) and abcd (blue)

adam concluded:
\its not possible to map abcd onto gfeh using a sequence of rigid transformations, so that quadrilaterals are not congruent.\
what error did adam make in his conclusion?

Explanation:

Rigid transformations (translation, rotation, reflection) preserve congruence. Adam didn't consider that a rotation (e.g., rotating ABCD or GFEH) plus translation/reflection could map one to the other. Congruent figures can be mapped via rigid transformations, so his mistake was not accounting for rotational transformations in the sequence.

Answer:

Adam failed to consider that a rotation (along with other rigid transformations like translation or reflection) could be part of the sequence to map \(ABCD\) onto \(GFEH\); congruent figures can be mapped using rigid transformations, so his conclusion that they are not congruent due to inability to map with rigid transformations (excluding rotation) is incorrect.