Printable math worksheet for students to practice writing congruence statements for pairs of triangles.

To solve the problem of completing the congruence statements for each pair of triangles, we need to identify the corresponding vertices and sides of the triangles based on their markings (such as angles and sides). The goal is to write the congruence statement in the form \( \Delta ABC \cong \Delta DEF \), where the order of the vertices indicates the correspondence between the triangles.

Let's go through each pair step by step:

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1)

- Triangles: \( \Delta ABC \) and \( \Delta DEF \)
- Markings:
- \( \angle C \) and \( \angle F \) are right angles.
- \( AB \cong DE \) (indicated by a single tick).
- \( BC \cong EF \) (indicated by a double tick).

Since the triangles have two sides and the included angle equal (SAS), they are congruent. The vertices must be matched accordingly:
- \( A \leftrightarrow D \)
- \( B \leftrightarrow E \)
- \( C \leftrightarrow F \)

Congruence Statement:
\[ \Delta ABC \cong \Delta DEF \]

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2)

- Triangles: \( \Delta JUV \) and \( \Delta YWX \)
- Markings:
- \( UV \cong WX \) (indicated by a single tick).
- \( VJ \cong XW \) (indicated by a double tick).
- \( \angle U \cong \angle W \) (indicated by a small arc).

Since the triangles have two sides and the included angle equal (SAS), they are congruent. The vertices must be matched accordingly:
- \( J \leftrightarrow Y \)
- \( U \leftrightarrow W \)
- \( V \leftrightarrow X \)

Congruence Statement:
\[ \Delta JUV \cong \Delta YWX \]

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3)

- Triangles: \( \Delta AFQ \) and \( \Delta RQC \)
- Markings:
- \( AQ \cong QR \) (indicated by a single tick).
- \( FQ \cong QC \) (indicated by a double tick).
- \( \angle A \cong \angle R \) (indicated by a small arc).

Since the triangles have two sides and the included angle equal (SAS), they are congruent. The vertices must be matched accordingly:
- \( A \leftrightarrow R \)
- \( F \leftrightarrow Q \)
- \( Q \leftrightarrow C \)

Congruence Statement:
\[ \Delta AFQ \cong \Delta RQC \]

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4)

- Triangles: \( \Delta KLM \) and \( \Delta GEF \)
- Markings:
- \( KL \cong GE \) (indicated by a single tick).
- \( LM \cong EF \) (indicated by a double tick).
- \( KM \cong GF \) (indicated by a triple tick).

Since all three sides are equal (SSS), the triangles are congruent. The vertices must be matched accordingly:
- \( K \leftrightarrow G \)
- \( L \leftrightarrow E \)
- \( M \leftrightarrow F \)

Congruence Statement:
\[ \Delta KLM \cong \Delta GEF \]

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5)

- Triangles: \( \Delta DEF \) and \( \Delta ZXY \)
- Markings:
- \( DE \cong ZX \) (indicated by a single tick).
- \( EF \cong XY \) (indicated by a double tick).
- \( \angle D \cong \angle Z \) (indicated by a small arc).

Since the triangles have two sides and the included angle equal (SAS), they are congruent. The vertices must be matched accordingly:
- \( D \leftrightarrow Z \)
- \( E \leftrightarrow X \)
- \( F \leftrightarrow Y \)

Congruence Statement:
\[ \Delta DEF \cong \Delta ZXY \]

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6)

- Triangles: \( \Delta TUV \) and \( \Delta VXW \)
- Markings:
- \( TU \cong VX \) (indicated by a single tick).
- \( UV \cong VW \) (indicated by a double tick).
- \( \angle T \cong \angle V \) (indicated by a small arc).

Since the triangles have two sides and the included angle equal (SAS), they are congruent. The vertices must be matched accordingly:
- \( T \leftrightarrow V \)
- \( U \leftrightarrow X \)
- \( V \leftrightarrow W \)

Congruence Statement:
\[ \Delta TUV \cong \Delta VXW \]

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7)

- Triangles: \( \Delta IKL \) and \( \Delta NMK \)
- Markings:
- \( IL \cong NK \) (indicated by a single tick).
- \( KL \cong MK \) (indicated by a double tick).
- \( \angle I \cong \angle N \) (indicated by a small arc).

Since the triangles have two sides and the included angle equal (SAS), they are congruent. The vertices must be matched accordingly:
- \( I \leftrightarrow N \)
- \( K \leftrightarrow M \)
- \( L \leftrightarrow K \)

Congruence Statement:
\[ \Delta IKL \cong \Delta NMK \]

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8)

- Triangles: \( \Delta CDE \) and \( \Delta FBA \)
- Markings:
- \( CD \cong FB \) (indicated by a single tick).
- \( DE \cong BA \) (indicated by a double tick).
- \( \angle C \cong \angle F \) (indicated by a small arc).

Since the triangles have two sides and the included angle equal (SAS), they are congruent. The vertices must be matched accordingly:
- \( C \leftrightarrow F \)
- \( D \leftrightarrow B \)
- \( E \leftrightarrow A \)

Congruence Statement:
\[ \Delta CDE \cong \Delta FBA \]

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Final Answers:

\[
\boxed{
\begin{array}{ll}
1) & \Delta ABC \cong \Delta DEF \\
2) & \Delta JUV \cong \Delta YWX \\
3) & \Delta AFQ \cong \Delta RQC \\
4) & \Delta KLM \cong \Delta GEF \\
5) & \Delta DEF \cong \Delta ZXY \\
6) & \Delta TUV \cong \Delta VXW \\
7) & \Delta IKL \cong \Delta NMK \\
8) & \Delta CDE \cong \Delta FBA \\
\end{array}
}
\]