Congruent Triangles worksheet with ASA, AAS, SAS, and SSS problems.

To solve the problem of identifying the congruent triangles and determining which postulate or theorem is being used, we need to analyze each pair of triangles based on the markings provided. The markings indicate corresponding sides and angles that are congruent. Here's the step-by-step solution for each problem:

1.

- Triangles: \( \Delta ABC \) and \( \Delta WIR \)
- Markings:
- \( AB \cong WI \)
- \( BC \cong IR \)
- \( \angle B \cong \angle I \)
- Reason: SAS (Side-Angle-Side)
- Answer: \( \Delta ABC \cong \Delta WIR \) by SAS

2.

- Triangles: \( \Delta ABC \) and \( \Delta SEC \)
- Markings:
- \( AB \cong SE \)
- \( \angle A \cong \angle S \)
- \( \angle C \cong \angle E \)
- Reason: ASA (Angle-Side-Angle)
- Answer: \( \Delta ABC \cong \Delta SEC \) by ASA

3.

- Triangles: \( \Delta ABC \) and \( \Delta NAG \)
- Markings:
- \( AB \cong NA \)
- \( BC \cong AG \)
- \( AC \cong NG \)
- Reason: SSS (Side-Side-Side)
- Answer: \( \Delta ABC \cong \Delta NAG \) by SSS

4.

- Triangles: \( \Delta GHJ \) and \( \Delta REH \)
- Markings:
- \( GH \cong RE \)
- \( HJ \cong EH \)
- \( \angle G \cong \angle R \)
- Reason: SAS (Side-Angle-Side)
- Answer: \( \Delta GHJ \cong \Delta REH \) by SAS

5.

- Triangles: \( \Delta ABC \) and \( \Delta ASD \)
- Markings:
- \( AB \cong AS \)
- \( \angle B \cong \angle S \)
- \( \angle C \cong \angle D \)
- Reason: AAS (Angle-Angle-Side)
- Answer: \( \Delta ABC \cong \Delta ASD \) by AAS

6.

- Triangles: \( \Delta ABC \) and \( \Delta HYE \)
- Markings:
- \( AB \cong HY \)
- \( \angle A \cong \angle H \)
- \( \angle C \cong \angle E \)
- Reason: AAS (Angle-Angle-Side)
- Answer: \( \Delta ABC \cong \Delta HYE \) by AAS

7.

- Triangles: \( \Delta ABC \) and \( \Delta ILH \)
- Markings:
- \( AB \cong IL \)
- \( BC \cong LH \)
- \( AC \cong IH \)
- Reason: SSS (Side-Side-Side)
- Answer: \( \Delta ABC \cong \Delta ILH \) by SSS

8.

- Triangles: \( \Delta DEF \) and \( \Delta NSM \)
- Markings:
- \( DE \cong NS \)
- \( EF \cong SM \)
- \( \angle E \cong \angle S \)
- Reason: SAS (Side-Angle-Side)
- Answer: \( \Delta DEF \cong \Delta NSM \) by SAS

9.

- Triangles: \( \Delta JKL \) and \( \Delta ATH \)
- Markings:
- \( JK \cong AT \)
- \( KL \cong TH \)
- \( JL \cong AH \)
- Reason: SSS (Side-Side-Side)
- Answer: \( \Delta JKL \cong \Delta ATH \) by SSS

10.

- Triangles: \( \Delta ABC \) and \( \Delta KGC \)
- Markings:
- \( AB \cong KG \)
- \( \angle A \cong \angle K \)
- \( \angle C \cong \angle G \)
- Reason: AAS (Angle-Angle-Side)
- Answer: \( \Delta ABC \cong \Delta KGC \) by AAS

11.

- Triangles: \( \Delta ABC \) and \( \Delta YDE \)
- Markings:
- \( AB \cong YD \)
- \( BC \cong DE \)
- \( \angle B \cong \angle D \)
- Reason: SAS (Side-Angle-Side)
- Answer: \( \Delta ABC \cong \Delta YDE \) by SAS

12.

- Triangles: \( \Delta MNO \) and \( \Delta SKA \)
- Markings:
- \( MN \cong SK \)
- \( NO \cong KA \)
- \( \angle N \cong \angle K \)
- Reason: SAS (Side-Angle-Side)
- Answer: \( \Delta MNO \cong \Delta SKA \) by SAS

Final Answer:

\[
\boxed{
\begin{array}{ll}
1. & \Delta ABC \cong \Delta WIR \text{ by SAS} \\
2. & \Delta ABC \cong \Delta SEC \text{ by ASA} \\
3. & \Delta ABC \cong \Delta NAG \text{ by SSS} \\
4. & \Delta GHJ \cong \Delta REH \text{ by SAS} \\
5. & \Delta ABC \cong \Delta ASD \text{ by AAS} \\
6. & \Delta ABC \cong \Delta HYE \text{ by AAS} \\
7. & \Delta ABC \cong \Delta ILH \text{ by SSS} \\
8. & \Delta DEF \cong \Delta NSM \text{ by SAS} \\
9. & \Delta JKL \cong \Delta ATH \text{ by SSS} \\
10. & \Delta ABC \cong \Delta KGC \text{ by AAS} \\
11. & \Delta ABC \cong \Delta YDE \text{ by SAS} \\
12. & \Delta MNO \cong \Delta SKA \text{ by SAS} \\
\end{array}
}
\]