Question

shonda was curious if segments ( overline{wx} ) and ( overline{yz} ) were congruent, so she tried to map one figure onto the other using transformations.

shonda concluded:

\its not possible to map ( overline{wx} ) onto ( overline{yz} ) using a sequence of rigid transformations, so the segments are not congruent.\

what error did shonda make in her conclusion?

choose 1 answer:

a one more transformation — a rotation — would map ( overline{wx} ) onto ( overline{yz} ). so the segments are congruent.

b one more transformation — a reflection — would map ( overline{wx} ) onto ( overline{yz} ). so the segments are congruent.

c there is no error. this is a correct conclusion.

Explanation:

To determine the error in Shonda's conclusion, we analyze rigid transformations (translations, rotations, reflections) which preserve segment length (congruence). $\overline{WX}$ and $\overline{YZ}$: after possible translation, a rotation can align their directions. Option A states a rotation maps $\overline{WX}$ to $\overline{YZ}$, proving congruence. Option B's reflection isn't needed here, and Option C is wrong as Shonda erred. So A is correct.

Answer:

A. One more transformation — a rotation — would map $\overline{WX}$ onto $\overline{YZ}$. So the segments are congruent.