Lennox was curious if triangles $ riangle A B E$ and $ riangle 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 $ riangle D C E$ onto $ riangle 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 $ riangle D C E$ onto $ riangle A B E$. So the triangles are similar.
(B) One more transformation - a dilation - would map $ riangle D C E$ onto $ riangle A B E$. So the triangles are similar.
(C) There is no error. This is a correct conclusion.

Question

Lennox was curious if triangles $	riangle A B E$ and $	riangle 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 $	riangle D C E$ onto $	riangle 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 $	riangle D C E$ onto $	riangle A B E$. So the triangles are similar.
(B) One more transformation - a dilation - would map $	riangle D C E$ onto $	riangle A B E$. So the triangles are similar.
(C) There is no error. This is a correct conclusion.

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To determine if two triangles are similar, we need to check if they can be mapped onto each other using a sequence of rigid transformations (rotations, reflections, translations) and dilations. ‖ ‖ 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 $ riangle DCE $ can be mapped onto triangle $ riangle 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 $ riangle DCE $ onto $ riangle 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.⚹◊What transformation did Lennox miss in mapping triangle DCE onto triangle ABE to show that they are similar?⍭ Generate me a similar question◊

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