Question

Math

Posted 6 months ago

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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.
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Answer from Sia

Posted 6 months ago

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.

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