Question

question 7 of 10
assume that \\( \triangle g h i \cong \triangle l m n \\). which of the following
congruence statements are correct? check all that apply.
a. \\( \angle n \cong \angle h \\)
b. \\( \overline{i h} \cong \overline{n m} \\)
c. \\( \angle m \cong \angle h \\)
d. \\( \overline{i h} \cong \overline{l m} \\)
e. \\( \overline{g h} \cong \overline{n m} \\)
f. \\( \angle l \cong \angle g \\)

Explanation:

Step1: Analyze congruent triangles properties

When \(\triangle GHI\cong\triangle LMN\), corresponding parts (angles and sides) are congruent. That is \(\angle G\cong\angle L\), \(\angle H\cong\angle M\), \(\angle I\cong\angle N\), \(\overline{GH}\cong\overline{LM}\), \(\overline{HI}\cong\overline{MN}\), \(\overline{GI}\cong\overline{LN}\).

Step2: Check each option

• Option A: \(\angle N\cong\angle H\) is incorrect. Since \(\angle N\cong\angle I\) (from \(\triangle GHI\cong\triangle LMN\)).
• Option B: \(\overline{HI}\cong\overline{NM}\) is correct. Because \(\overline{HI}\) in \(\triangle GHI\) corresponds to \(\overline{MN}\) (same as \(\overline{NM}\)) in \(\triangle LMN\).
• Option C: \(\angle M\cong\angle H\) is incorrect. \(\angle M\) corresponds to \(\angle H\) but the order is wrong. It should be \(\angle H\cong\angle M\).
• Option D: \(\overline{HI}\cong\overline{LM}\) is incorrect. \(\overline{HI}\cong\overline{MN}\) and \(\overline{GH}\cong\overline{LM}\).
• Option E: \(\overline{GH}\cong\overline{NM}\) is incorrect. \(\overline{GH}\cong\overline{LM}\) and \(\overline{HI}\cong\overline{MN}\).
• Option F: \(\angle L\cong\angle G\) is correct. As \(\angle G\) in \(\triangle GHI\) corresponds to \(\angle L\) in \(\triangle LMN\).

Answer:

B. \(\overline{HI}\cong\overline{NM}\), F. \(\angle L\cong\angle G\)