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This question asks for identifying correct congruence statements based on the information that \( \triangle GHI \cong \triangle LMN \). When two triangles are congruent, corresponding sides and angles are equal.

To solve, let's match the vertices of the triangles \( \triangle GHI \) and \( \triangle LMN \):

- \( G \leftrightarrow L \)
- \( H \leftrightarrow M \)
- \( I \leftrightarrow N \)

Now, let's check each statement:

- **A. \( \overline{IH} \cong \overline{LM} \)**: This is **incorrect**. \( IH \) should correspond to \( MN \), not \( LM \).
- **B. \( \angle M \cong \angle H \)**: This is **correct**, as \( H \) corresponds to \( M \).
- **C. \( \overline{GH} \cong \overline{MN} \)**: This is **incorrect**. \( GH \) corresponds to \( LM \), not \( MN \).
- **D. \( \angle N \cong \angle H \)**: This is **incorrect**, as \( N \) corresponds to \( I \), not \( H \).
- **E. \( \angle L \cong \angle G \)**: This is **correct**, as \( G \) corresponds to \( L \).
- **F. \( \overline{IH} \cong \overline{NM} \)**: This is **correct**, as \( IH \) corresponds to \( NM \).

So, the correct statements are **B**, **E**, and **F**.

Would you like further clarification or more details?

Here are five related questions to expand your understanding:
1. How do you determine which sides or angles are corresponding between congruent triangles?
2. What are the different postulates to prove two triangles are congruent?
3. Can two triangles be congruent if only two pairs of sides are equal?
4. What are the key differences between congruence and similarity in triangles?
5. How does the angle-side-angle (ASA) congruence postulate work?

**Tip:** When analyzing congruent triangles, always compare the order of vertices to identify corresponding parts correctly.

Assume that ∆GHI ≅ ∆LMN. Which of the following congruence statements are correct? Check all that apply.

Explore the properties of congruent triangles with a focus on ∆GHI and ∆LMN. Learn how to identify correct congruence statements, compare corresponding angles and sides, and understand key concepts in triangle congruence. Suitable for Grades 8-10.

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