Problem

Vertex correspondences are \(A~\leftrightarrow~D,~B~\leftrightarrow~E,~\text{and}~C~\leftrightarrow~F\). Write the ordered similarity statement so every position preserves its supplied match, then verify the \(\text{three}~\text{side}~\text{correspondences}\) implied by that order.

Unworked triangles ABC and DEF with first matching arc marks at A and D, second matching arcs at B and E, and third matching arcs at C and F; the ordered similarity statement is withheld.

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A similarity statement must preserve every supplied vertex match position by position. We’ll list the three mappings, assemble the triangle names in the same order, derive each side correspondence by mapping both endpoints, and use those side pairs to audit the final notation.

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Since A matches D, B matches E, and C matches F, the first triangle should be reordered as △ACB, so △ACB ~ △DEF.

Since A matches D, B matches E, and C matches F, the second triangle can be written as △DFE, so △ABC ~ △DFE.

Since the triangles are similar, the order does not matter, so any arrangement like △ABC ~ △EFD is acceptable.

Since A matches D, B matches E, and C matches F, the letters line up in the same order, so △ABC ~ △DEF.

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Vertex correspondences are \(A~\leftrightarrow~D,~B~\leftrightarrow~E,~\text{and}~C~\leftrightarrow~F\). Write the ordered similarity statement so every position preserves its supplied match, then verify the \(\text{three}~\text{side}~\text{correspondences}\) implied by that order.

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