Question

kelsey was curious if △ abc was congruent to △ fed, so she tried to map one triangle onto the other using transformations:

kelsey concluded:
\its not possible to map △ abc onto △ fed using a sequence of rigid transformations, so the triangles are not congruent.\
what error did kelsey make in her conclusion?

Explanation:

Rigid transformations (translation, rotation, reflection) preserve congruence. Kelsey likely missed that a rotation (and maybe other transformations) can map \( \triangle ABC \) to \( \triangle FED \). Congruent triangles can be mapped via rigid transformations, so her conclusion that it's impossible (and thus they aren't congruent) is wrong—she failed to consider all rigid transformation sequences.

Answer:

Kelsey erred by concluding the triangles aren't congruent because she thought mapping via rigid transformations was impossible, but \( \triangle ABC \) can be mapped to \( \triangle FED \) using rigid transformations (e.g., rotation), so they are congruent.