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suppose \\( \\triangle def \\cong \\triangle mno \\) which congruency s…

Question

suppose \\( \triangle def \cong \triangle mno \\)
which congruency statement is true?
\\( \overline { e f } \cong \overline { m n } \\)
\\( \overline { d e } \cong \overline { m n } \\)
\\( \overline { d f } \cong \overline { n o } \\)
\\( \overline { e f } \cong \overline { m o } \\)

Explanation:

Step1: Recall the property of congruent triangles

When \(\triangle DEF\cong\triangle MNO\), the corresponding parts are congruent. That is \(DE = MN\), \(EF=NO\), \(DF = MO\), \(\angle D=\angle M\), \(\angle E=\angle N\), \(\angle F=\angle O\)

Step2: Check each option

  • For \(\overline{EF}\cong\overline{MN}\): Since \(EF = NO\) (from \(\triangle DEF\cong\triangle MNO\)), this is false.
  • For \(\overline{DE}\cong\overline{MN}\): Since \(DE = MN\) (from \(\triangle DEF\cong\triangle MNO\)), this is true.
  • For \(\overline{DF}\cong\overline{NO}\): Since \(DF = MO\) (from \(\triangle DEF\cong\triangle MNO\)), this is false.
  • For \(\overline{EF}\cong\overline{MO}\): Since \(EF = NO\) (from \(\triangle DEF\cong\triangle MNO\)), this is false.

Answer:

\(\overline{DE}\cong\overline{MN}\)