Problem

Complete the similarity proof from \(\angle~A~\cong~\angle~D\) and \(\angle~B~\cong~\angle~E\). State the \(\text{two}~\angle~\text{pairs}\), derive the remaining vertex correspondence, write the triangles in matching order, and name the \(AA\) criterion.

Unworked diagrams of triangles ABC and DEF with matching arc marks on ∠A and ∠D and on ∠B and ∠E; no third-angle mapping or AA conclusion is shown.

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What this problem is really about

A complete AA proof needs two explicit angle pairs and an ordered correspondence. We’ll state both givens, record their vertex mappings, assign the only remaining vertex pair, place corresponding letters in matching positions, and cite AA without introducing any unsupported side relationship.

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Triangle ABC is similar to triangle DEF by AA similarity because they have two equal sides and one equal angle.

Triangle ABC is similar to triangle DEF by AA similarity because angle A matches angle D and angle B matches angle E.

Triangle ADE is similar to triangle ABC by AA similarity because angle A matches angle D and angle B matches angle E.

Triangle ABC is similar to triangle DFE by AA similarity because angle A matches angle D and angle B matches angle E.

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Complete the similarity proof from \(\angle~A~\cong~\angle~D\) and \(\angle~B~\cong~\angle~E\). State the \(\text{two}~\angle~\text{pairs}\), derive the remaining vertex correspondence, write the triangles in matching order, and name the \(AA\) criterion.

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