Question

which congruency statement is true?

○ ef ≅ mn

○ ef ≅ mo

○ df ≅ no

○ de ≅ mn

Explanation:

To determine the correct congruency statement, we analyze each option by recalling that congruent segments have the same length and are corresponding parts of congruent figures (though the figures aren’t shown, we assume standard congruency logic for segments):

1. Option 1: \( \boldsymbol{\overline{EF} \cong \overline{MN}} \)

If \( \overline{EF} \) and \( \overline{MN} \) are corresponding congruent segments (e.g., from congruent triangles or figures), this could hold.

1. Option 2: \( \boldsymbol{\overline{EF} \cong \overline{MO}} \)

\( \overline{EF} \) and \( \overline{MO} \) likely do not correspond (different vertex labels), so this is false.

1. Option 3: \( \boldsymbol{\overline{DF} \cong \overline{NO}} \)

\( \overline{DF} \) and \( \overline{NO} \) have mismatched vertices (D, F vs. N, O), so they are not corresponding congruent segments.

1. Option 4: \( \boldsymbol{\overline{DE} \cong \overline{MN}} \)

\( \overline{DE} \) and \( \overline{MN} \) have mismatched vertices (D, E vs. M, N), so they are not corresponding congruent segments.

Among the options, \( \overline{EF} \cong \overline{MN} \) is the only one where the segment labels suggest corresponding congruent parts (assuming standard congruency notation for segments).

Answer:

\( \boldsymbol{\overline{EF} \cong \overline{MN}} \) (the first option: \( \boldsymbol{EF \cong MN} \))