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finding corresponding parts given congruent triangles \\( \\triangle ab…

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} \\)

Explanation:

Brief Explanations

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 \(\angle M\)).

Answer:

\(\overline{AB}\) and \(\overline{MN}\), \(\angle B\) and \(\angle N\), \(\overline{CB}\) and \(\overline{LN}\)