Layla was able to map circle $M$ onto circle $N$ using a translation and a dilation.

Layla concluded:
"I was able to map circle $M$ onto circle $N$ using a sequence of rigid transformations, so the figures are congruent."

What error did Layla make in her conclusion?
Choose 1 answer:
(A) Layla didn't use only rigid transformations, so the figures are not congruent.
(B) It's possible to map circle $M$ onto circle $N$ using a sequence of rigid transformations, but the figures are not congruent.
(C) There is no error. This is a correct conclusion.

Question

Layla was able to map circle $M$ onto circle $N$ using a translation and a dilation.

Layla concluded:
"I was able to map circle $M$ onto circle $N$ using a sequence of rigid transformations, so the figures are congruent."

What error did Layla make in her conclusion?
Choose 1 answer:
(A) Layla didn't use only rigid transformations, so the figures are not congruent.
(B) It's possible to map circle $M$ onto circle $N$ using a sequence of rigid transformations, but the figures are not congruent.
(C) There is no error. This is a correct conclusion.

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Identify the types of transformations used by Layla. ‖ ‖ step 2 ⋮ Recognize that a translation is a rigid transformation, which does not change the size or shape of a figure. ‖ ‖ step 3 ⋮ Acknowledge that a dilation is not a rigid transformation because it changes the size of the figure. ‖ ‖ step 4 ⋮ Understand that congruent figures must have the same size and shape, which is preserved only through rigid transformations. ‖ ‖ step 5 ⋮ Conclude that since a dilation was used, the figures cannot be congruent. ‖ ∻Answer∻ ⚹ (A) Layla didn't use only rigid transformations, so the figures are not congruent. ⚹ ∻Key Concept∻ ⚹Rigid Transformations and Congruence⚹ ∻Explanation∻ ⚹Rigid transformations include translations, rotations, and reflections, which do not alter the size or shape of a figure. Dilation, which changes the size of the figure, is not a rigid transformation. Therefore, if a dilation is used, the figures cannot be congruent.⚹◊What are the properties of rigid transformations in geometry?⍭ Generate me a similar question◊

Sia