Corresponding Parts of Congruent Triangles Are Congruent Worksheet ... - Free Printable

To solve the problem, we need to identify which parts of the triangles in each pair are congruent based on the given postulate (SSS, SAS, AAS, ASA, or HL). Let's analyze each pair step by step.

1. SSS (Side-Side-Side)

- Given: All three sides of one triangle are marked as congruent to the corresponding sides of the other triangle.
- Triangles: \( \triangle ABC \cong \triangle CDA \)
- Explanation: The sides \( AB \cong CD \), \( BC \cong DA \), and \( AC \cong CA \) (reflexive property).

2. AAS (Angle-Angle-Side)

- Given: Two angles and a non-included side of one triangle are congruent to the corresponding parts of the other triangle.
- Triangles: \( \triangle POR \cong \triangle QOS \)
- Explanation: The angles \( \angle P \cong \angle Q \), \( \angle R \cong \angle S \), and the side \( OR \cong OS \).

3. SSS (Side-Side-Side)

- Given: All three sides of one triangle are marked as congruent to the corresponding sides of the other triangle.
- Triangles: \( \triangle EFG \cong \triangle FGH \)
- Explanation: The sides \( EF \cong FG \), \( FG \cong GH \), and \( EG \cong FH \).

4. SAS (Side-Angle-Side)

- Given: Two sides and the included angle of one triangle are congruent to the corresponding parts of the other triangle.
- Triangles: \( \triangle XYG \cong \triangle HGF \)
- Explanation: The sides \( XY \cong HG \), \( YG \cong GF \), and the included angle \( \angle XYG \cong \angle HGF \).

5. SAS (Side-Angle-Side)

- Given: Two sides and the included angle of one triangle are congruent to the corresponding parts of the other triangle.
- Triangles: \( \triangle PQR \cong \triangle STR \)
- Explanation: The sides \( PQ \cong ST \), \( QR \cong TR \), and the included angle \( \angle PQR \cong \angle STR \).

6. ASA (Angle-Side-Angle)

- Given: Two angles and the included side of one triangle are congruent to the corresponding parts of the other triangle.
- Triangles: \( \triangle ABC \cong \triangle CDA \)
- Explanation: The angles \( \angle BAC \cong \angle DCA \), \( \angle ACB \cong \angle CAD \), and the included side \( AC \cong CA \) (reflexive property).

7. SAS (Side-Angle-Side)

- Given: Two sides and the included angle of one triangle are congruent to the corresponding parts of the other triangle.
- Triangles: \( \triangle XYZ \cong \triangle WZY \)
- Explanation: The sides \( XY \cong WZ \), \( YZ \cong ZY \) (reflexive property), and the included angle \( \angle XYZ \cong \angle WZY \).

8. HL (Hypotenuse-Leg)

- Given: The hypotenuse and one leg of a right triangle are congruent to the corresponding parts of another right triangle.
- Triangles: \( \triangle ABC \cong \triangle ADC \)
- Explanation: The hypotenuse \( AB \cong AD \), the leg \( BC \cong DC \), and both triangles are right triangles with the right angle at \( C \).

Final Answers

1. \( \triangle ABC \cong \triangle CDA \)
2. \( \triangle POR \cong \triangle QOS \)
3. \( \triangle EFG \cong \triangle FGH \)
4. \( \triangle XYG \cong \triangle HGF \)
5. \( \triangle PQR \cong \triangle STR \)
6. \( \triangle ABC \cong \triangle CDA \)
7. \( \triangle XYZ \cong \triangle WZY \)
8. \( \triangle ABC \cong \triangle ADC \)

\[
\boxed{
\begin{array}{ll}
1. & \triangle ABC \cong \triangle CDA \\
2. & \triangle POR \cong \triangle QOS \\
3. & \triangle EFG \cong \triangle FGH \\
4. & \triangle XYG \cong \triangle HGF \\
5. & \triangle PQR \cong \triangle STR \\
6. & \triangle ABC \cong \triangle CDA \\
7. & \triangle XYZ \cong \triangle WZY \\
8. & \triangle ABC \cong \triangle ADC \\
\end{array}
}
\]