Worksheet - Congruent Triangles - Free Printable

To solve the problem of determining whether the triangles are congruent and identifying the appropriate congruence theorem or postulate, we need to analyze each pair of triangles step by step. Below is the detailed solution for each part:

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1)

Triangles: \( \Delta ABD \) and \( \Delta CDB \)

- Analysis:
- Both triangles share the side \( BD \).
- \( AB = CD \) (given in the diagram).
- \( AD = CB \) (given in the diagram).
- The included angle between \( AB \) and \( AD \) is \( \angle A \), and the included angle between \( CD \) and \( CB \) is \( \angle C \). These angles appear to be equal based on the diagram.

- Conclusion:
- The triangles satisfy the Side-Angle-Side (SAS) congruence criterion.
- Therefore, \( \Delta ABD \cong \Delta CDB \).

- Congruence: \( \Delta ABD \cong \Delta CDB \)
- Reason: SAS

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2)

Triangles: \( \Delta EFG \) and \( \Delta KJG \)

- Analysis:
- Both triangles share the side \( FG \).
- \( EF = KJ \) (given in the diagram).
- \( EG = KG \) (given in the diagram).
- The included angle between \( EF \) and \( EG \) is \( \angle E \), and the included angle between \( KJ \) and \( KG \) is \( \angle K \). These angles appear to be equal based on the diagram.

- Conclusion:
- The triangles satisfy the Side-Angle-Side (SAS) congruence criterion.
- Therefore, \( \Delta EFG \cong \Delta KJG \).

- Congruence: \( \Delta EFG \cong \Delta KJG \)
- Reason: SAS

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3)

Triangles: \( \Delta EMN \) and \( \Delta QPN \)

- Analysis:
- Both triangles share the side \( MN \).
- \( EM = QP \) (given in the diagram).
- \( EN = QN \) (given in the diagram).
- The included angle between \( EM \) and \( EN \) is \( \angle MNE \), and the included angle between \( QP \) and \( QN \) is \( \angle PNQ \). These angles appear to be equal based on the diagram.

- Conclusion:
- The triangles satisfy the Side-Angle-Side (SAS) congruence criterion.
- Therefore, \( \Delta EMN \cong \Delta QPN \).

- Congruence: \( \Delta EMN \cong \Delta QPN \)
- Reason: SAS

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4)

Triangles: \( \Delta STU \) and \( \Delta VUT \)

- Analysis:
- Both triangles share the side \( TU \).
- \( ST = VU \) (given in the diagram).
- \( SU = VT \) (given in the diagram).
- The included angle between \( ST \) and \( SU \) is \( \angle S \), and the included angle between \( VU \) and \( VT \) is \( \angle V \). These angles appear to be equal based on the diagram.

- Conclusion:
- The triangles satisfy the Side-Angle-Side (SAS) congruence criterion.
- Therefore, \( \Delta STU \cong \Delta VUT \).

- Congruence: \( \Delta STU \cong \Delta VUT \)
- Reason: SAS

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5)

Triangles: \( \Delta YZA \) and \( \Delta BZA \)

- Analysis:
- Both triangles share the side \( ZA \).
- \( YZ = BZ \) (given in the diagram).
- \( YA = BA \) (given in the diagram).
- The included angle between \( YZ \) and \( YA \) is \( \angle Y \), and the included angle between \( BZ \) and \( BA \) is \( \angle B \). These angles appear to be equal based on the diagram.

- Conclusion:
- The triangles satisfy the Side-Angle-Side (SAS) congruence criterion.
- Therefore, \( \Delta YZA \cong \Delta BZA \).

- Congruence: \( \Delta YZA \cong \Delta BZA \)
- Reason: SAS

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6)

Triangles: \( \Delta CDE \) and \( \Delta GFE \)

- Analysis:
- Both triangles share the side \( DE \).
- \( CD = GF \) (given in the diagram).
- \( CE = GE \) (given in the diagram).
- The included angle between \( CD \) and \( CE \) is \( \angle DCE \), and the included angle between \( GF \) and \( GE \) is \( \angle FGE \). These angles appear to be equal based on the diagram.

- Conclusion:
- The triangles satisfy the Side-Angle-Side (SAS) congruence criterion.
- Therefore, \( \Delta CDE \cong \Delta GFE \).

- Congruence: \( \Delta CDE \cong \Delta GFE \)
- Reason: SAS

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Final Answer:

\[
\boxed{
\begin{array}{ll}
1) & \Delta ABD \cong \Delta CDB \quad \text{(SAS)} \\
2) & \Delta EFG \cong \Delta KJG \quad \text{(SAS)} \\
3) & \Delta EMN \cong \Delta QPN \quad \text{(SAS)} \\
4) & \Delta STU \cong \Delta VUT \quad \text{(SAS)} \\
5) & \Delta YZA \cong \Delta BZA \quad \text{(SAS)} \\
6) & \Delta CDE \cong \Delta GFE \quad \text{(SAS)}
\end{array}
}
\]