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This worksheet is asking to complete congruence statements for each pair of triangles. To do that, we can match the corresponding sides and angles of the triangles based on the markings given.

Here are the solutions for each congruence statement:

1. **\( \triangle ABC \cong \triangle DEF \)**  
   Corresponding parts are:  
   - \( A \leftrightarrow D \)  
   - \( B \leftrightarrow E \)  
   - \( C \leftrightarrow F \)

2. **\( \triangle UVW \cong \triangle ZXY \)**  
   Corresponding parts are:  
   - \( U \leftrightarrow Z \)  
   - \( V \leftrightarrow X \)  
   - \( W \leftrightarrow Y \)

3. **\( \triangle PQR \cong \triangle STR \)**  
   Corresponding parts are:  
   - \( P \leftrightarrow S \)  
   - \( Q \leftrightarrow T \)  
   - \( R \leftrightarrow R \) (common vertex)

4. **\( \triangle KLM \cong \triangle GFE \)**  
   Corresponding parts are:  
   - \( K \leftrightarrow G \)  
   - \( L \leftrightarrow F \)  
   - \( M \leftrightarrow E \)

5. **\( \triangle DEF \cong \triangle XYZ \)**  
   Corresponding parts are:  
   - \( D \leftrightarrow Y \)  
   - \( E \leftrightarrow X \)  
   - \( F \leftrightarrow Z \)

6. **\( \triangle TUV \cong \triangle WXU \)**  
   Corresponding parts are:  
   - \( T \leftrightarrow W \)  
   - \( U \leftrightarrow X \)  
   - \( V \leftrightarrow U \)

7. **\( \triangle JKL \cong \triangle NML \)**  
   Corresponding parts are:  
   - \( J \leftrightarrow N \)  
   - \( K \leftrightarrow M \)  
   - \( L \leftrightarrow L \) (common vertex)

8. **\( \triangle CDE \cong \triangle FDE \)**  
   Corresponding parts are:  
   - \( C \leftrightarrow F \)  
   - \( D \leftrightarrow D \) (common vertex)  
   - \( E \leftrightarrow E \) (common vertex)

Would you like further clarification or details on how these pairs were determined?

Here are 5 related questions to expand on this:

1. How do you identify corresponding parts between two congruent triangles?
2. What are the criteria (SSS, SAS, ASA, AAS) for triangle congruence?
3. Can you explain why angle markings and side markings help determine congruence?
4. What does the statement \( \triangle ABC \cong \triangle DEF \) mean geometrically?
5. Are there any situations where two triangles with identical side lengths aren't congruent?

**Tip**: When determining congruence, focus on matching sides and angles using the given markings carefully, as they reveal how each triangle's parts correspond to another.

Complete the congruence statement for each pair of triangles.

This worksheet helps students practice completing congruence statements for pairs of triangles using geometric reasoning. Suitable for middle school students (Grades 7-9). Focuses on recognizing corresponding sides and angles based on given markings.

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