Question

eleanor was curious if triangles $\triangle def$ and $\triangle ghi$ were similar, so she tried to map one figure onto the other using rigid transformations.

eleanor concluded:
\its not possible to map $\triangle def$ onto $\triangle ghi$ using a sequence of rigid transformations, so the triangles are not similar.\
what error did eleanor make in her conclusion?
choose 1 answer:
\\(\boldsymbol{\text{a}}\\) one more transformation — a rotation — would map $\triangle def$ onto $\triangle ghi$. so the triangles are similar.
\\(\boldsymbol{\text{b}}\\) one more transformation — a dilation — would map $\triangle def$ onto $\triangle ghi$. so the triangles are similar.
\\(\boldsymbol{\text{c}}\\) there is no error. this is a correct conclusion.

Explanation:

To determine triangle similarity, we can use rigid transformations (translation, rotation, reflection) and dilations. Rigid transformations preserve shape and size (congruence), while dilations change size but preserve shape (similarity). Eleanor only considered rigid transformations, but similarity allows dilations. $\triangle DEF$ and $\triangle GHI$ have the same shape but different sizes, so a dilation (scaling) would map one to the other, making them similar. Option A is incorrect because rotation is a rigid transformation (preserves size), and the triangles are not the same size. Option C is incorrect as Eleanor's conclusion is wrong because she didn't consider dilations for similarity. Option B correctly identifies that a dilation (which is allowed for similarity) is needed, not just rigid transformations.

Answer:

B. One more transformation — a dilation — would map $\triangle DEF$ onto $\triangle GHI$. So the triangles are similar.