Problem

Vertex correspondences are \(L~\leftrightarrow~N\), \(M~\leftrightarrow~P\), and \(K~\leftrightarrow~Q\). 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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Since L matches N, M matches P, and K matches Q, any order of those matching letters shows similarity, so △LMK ~ △QPN also works.

Since L matches N, M matches P, and K matches Q, the second triangle can be written alphabetically, so △LMK ~ △NQP.

Since L matches N, M matches P, and K matches Q, the order stays aligned, so △LMK ~ △NPQ.

Since L matches N, M matches P, and K matches Q, the first triangle should be rearranged to fit, so △LKM ~ △NPQ.

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