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 two quadrilaterals on a grid
adam concluded:
\its not possible to map (abcd) onto (gfeh) using a sequence of rigid transformations, so the quadrilaterals are not congruent.\
what error did adam make in his conclusion?
choose 1 answer:
a one more transformation — a rotation — would map (abcd) onto (gfeh). so the quadrilaterals are congruent.
b one more transformation — a reflection — would map (abcd) onto (gfeh). so the quadrilaterals are congruent.
c there is no error. this is a correct conclusion.

Explanation:

To determine congruence via rigid transformations (translations, rotations, reflections), we analyze the figures. Adam thought no rigid transformations work, but a reflection (a rigid transformation) can map \(ABCD\) to \(GFEH\) by flipping over a line to align the shapes. So his error was not considering a reflection as a valid rigid transformation to complete the mapping. Option B correctly identifies this: a reflection would map \(ABCD\) onto \(GFEH\), proving congruence.

Answer:

B. One more transformation — a reflection — would map \(ABCD\) onto \(GFEH\). So the quadrilaterals are congruent.