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Question
Math
Posted 6 months ago

Lennox was curious if triangles ABE\triangle A B E and DCE\triangle D C E were similar, so she tried to map one figure onto the other using a reflection and a dilation.

Lennox concluded:
"It's not possible to map DCE\triangle D C E onto ABE\triangle A B E using a sequence of rigid transformations and dilations, so the triangles are not similar."

What error did Lennox make in her conclusion?

Choose 1 answer:
(A) One more transformation - a horizontal stretch - would map DCE\triangle D C E onto ABE\triangle A B E. So the triangles are similar.
(B) One more transformation - a dilation - would map DCE\triangle D C E onto ABE\triangle A B E. So the triangles are similar.
(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 2
A rigid transformation preserves the shape and size of a figure, while a dilation changes the size but not the shape
step 3
If triangle DCE \triangle DCE can be mapped onto triangle ABE \triangle ABE using these transformations, then they are similar
step 4
Lennox's conclusion that the triangles are not similar because they cannot be mapped onto each other using a sequence of rigid transformations and dilations is incorrect if there exists a sequence of transformations that can do so
step 5
A horizontal stretch is not a rigid transformation or a dilation, so it cannot be used to prove similarity
step 6
If a dilation alone can map DCE \triangle DCE onto ABE \triangle ABE , then the triangles are similar
step 7
Since the question implies that Lennox may have missed a possible transformation, we need to consider whether a dilation could map one triangle onto the other
B
Key Concept
Similar Triangles
Explanation
Two triangles are similar if one can be mapped onto the other using a sequence of rigid transformations and dilations. A horizontal stretch is not a valid transformation to prove similarity.

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