Congruent Triangles Worksheet with labeled triangles for identifying corresponding sides and angles.

Problem Analysis:

The task involves identifying the corresponding sides and angles for each congruence statement. Congruent triangles have equal corresponding sides and angles. The notation for congruence is written as \( \triangle ABC \cong \triangle DEF \), where the order of the vertices indicates the correspondence.

#### Given:
1. \( \triangle TUV \cong \triangle GFE \)
2. \( \triangle WVU \cong \triangle GHI \)

We need to determine the corresponding sides and angles for each congruence statement.

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Solution:

#### 1. \( \triangle TUV \cong \triangle GFE \)

- Corresponding Vertices:
- \( T \) corresponds to \( G \)
- \( U \) corresponds to \( F \)
- \( V \) corresponds to \( E \)

- Corresponding Sides:
- \( TU \) corresponds to \( GF \)
- \( UV \) corresponds to \( FE \)
- \( VT \) corresponds to \( EG \)

- Corresponding Angles:
- \( \angle T \) corresponds to \( \angle G \)
- \( \angle U \) corresponds to \( \angle F \)
- \( \angle V \) corresponds to \( \angle E \)

#### 2. \( \triangle WVU \cong \triangle GHI \)

- Corresponding Vertices:
- \( W \) corresponds to \( G \)
- \( V \) corresponds to \( H \)
- \( U \) corresponds to \( I \)

- Corresponding Sides:
- \( WV \) corresponds to \( GH \)
- \( VU \) corresponds to \( HI \)
- \( UW \) corresponds to \( IG \)

- Corresponding Angles:
- \( \angle W \) corresponds to \( \angle G \)
- \( \angle V \) corresponds to \( \angle H \)
- \( \angle U \) corresponds to \( \angle I \)

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Final Answer:

\[
\boxed{
\begin{aligned}
1. & \quad \text{Corresponding sides: } TU \leftrightarrow GF, \, UV \leftrightarrow FE, \, VT \leftrightarrow EG \\
& \quad \text{Corresponding angles: } \angle T \leftrightarrow \angle G, \, \angle U \leftrightarrow \angle F, \, \angle V \leftrightarrow \angle E \\
2. & \quad \text{Corresponding sides: } WV \leftrightarrow GH, \, VU \leftrightarrow HI, \, UW \leftrightarrow IG \\
& \quad \text{Corresponding angles: } \angle W \leftrightarrow \angle G, \, \angle V \leftrightarrow \angle H, \, \angle U \leftrightarrow \angle I
\end{aligned}
}
\]