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Question
finding corresponding parts given congruent triangles \\( \triangle abc \\) and \\( \triangle mnl \\), which of the following are corresponding parts? check all that apply. \\( \angle a \\) and \\( \angle l \\) \\( \overline{ab} \\) and \\( \overline{mn} \\) \\( \angle c \\) and \\( \angle m \\) \\( \overline{ac} \\) and \\( \overline{ln} \\) \\( \angle b \\) and \\( \angle n \\) \\( \overline{cb} \\) and \\( \overline{ln} \\)
When two triangles are congruent, their corresponding vertices, angles, and sides are equal. For \(\triangle ABC\) and \(\triangle MNL\), we match the vertices in the order of the triangle names.
- For sides: The order of the letters in the side - segment notation matters. If \(\triangle ABC\cong\triangle MNL\), then \(A\) corresponds to \(M\), \(B\) corresponds to \(N\), and \(C\) corresponds to \(L\). So, \(\overline{AB}\) corresponds to \(\overline{MN}\) (since \(A\to M\) and \(B\to N\)), \(\overline{AC}\) corresponds to \(\overline{ML}\) (but \(\overline{AC}\) and \(\overline{LN}\) is incorrect as \(C\to L\) and \(A\to M\)), \(\overline{CB}\) corresponds to \(\overline{LN}\) (since \(C\to L\) and \(B\to N\)).
- For angles: \(\angle A\) corresponds to \(\angle M\) (not \(\angle L\)), \(\angle B\) corresponds to \(\angle N\), \(\angle C\) corresponds to \(\angle L\) (not \(\angle M\)).
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\(\overline{AB}\) and \(\overline{MN}\), \(\angle B\) and \(\angle N\), \(\overline{CB}\) and \(\overline{LN}\)