Triangle Congruence Worksheet.pdf - Free Printable

To solve the problem, we need to determine which postulate or theorem can be used to conclude that each pair of triangles is congruent. The common postulates and theorems for triangle congruence are:

1. SSS (Side-Side-Side): If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
2. SAS (Side-Angle-Side): If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
3. ASA (Angle-Side-Angle): If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
4. AAS (Angle-Angle-Side): If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.
5. HL (Hypotenuse-Leg): If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Now, let's analyze each pair of triangles:

1.

- Triangles: \( \triangle FGH \) and \( \triangle IJH \)
- Given: \( FG \cong IJ \), \( GH \cong JH \), \( FH \cong IH \)
- Postulate/Theorem: SSS
- Reason: All three sides are congruent.

2.

- Triangles: \( \triangle NOP \) and \( \triangle QRP \)
- Given: \( NO \cong QR \), \( OP \cong RP \), \( \angle NOP \cong \angle QRP \)
- Postulate/Theorem: SAS
- Reason: Two sides and the included angle are congruent.

3.

- Triangles: \( \triangle ABC \) and \( \triangle DEC \)
- Given: \( AB \cong DE \), \( BC \cong EC \), \( \angle ABC \cong \angle DEC \)
- Postulate/Theorem: SAS
- Reason: Two sides and the included angle are congruent.

4.

- Triangles: \( \triangle RST \) and \( \triangle UTS \)
- Given: \( RS \cong UT \), \( ST \cong TS \), \( \angle RST \cong \angle UTS \)
- Postulate/Theorem: ASA
- Reason: Two angles and the included side are congruent.

5.

- Triangles: \( \triangle JKL \) and \( \triangle MLK \)
- Given: \( JK \cong ML \), \( KL \cong LK \), \( \angle JKL \cong \angle MLK \)
- Postulate/Theorem: ASA
- Reason: Two angles and the included side are congruent.

6.

- Triangles: \( \triangle NOP \) and \( \triangle QPO \)
- Given: \( NO \cong QP \), \( OP \cong PO \), \( \angle NOP \cong \angle QPO \)
- Postulate/Theorem: AAS
- Reason: Two angles and a non-included side are congruent.

7.

- Triangles: \( \triangle ABC \) and \( \triangle DCE \)
- Given: \( AB \cong DC \), \( BC \cong CE \), \( \angle ABC \cong \angle DCE \)
- Postulate/Theorem: SAS
- Reason: Two sides and the included angle are congruent.

8.

- Triangles: \( \triangle FGH \) and \( \triangle HGF \)
- Given: \( FG \cong HG \), \( GH \cong GF \), \( \angle FGH \cong \angle HGF \)
- Postulate/Theorem: SSS
- Reason: All three sides are congruent.

9.

- Triangles: \( \triangle JKL \) and \( \triangle MLK \)
- Given: \( JK \cong ML \), \( KL \cong LK \), \( \angle JKL \cong \angle MLK \)
- Postulate/Theorem: ASA
- Reason: Two angles and the included side are congruent.

10.

- Triangles: \( \triangle NOP \) and \( \triangle QPN \)
- Given: \( NO \cong QP \), \( OP \cong PN \), \( \angle NOP \cong \angle QPN \)
- Postulate/Theorem: AAS
- Reason: Two angles and a non-included side are congruent.

11.

- Triangles: \( \triangle JKL \) and \( \triangle MLK \)
- Given: \( JK \cong ML \), \( KL \cong LK \), \( \angle JKL \cong \angle MLK \)
- Postulate/Theorem: ASA
- Reason: Two angles and the included side are congruent.

12.

- Triangles: \( \triangle RST \) and \( \triangle TUR \)
- Given: \( RS \cong TU \), \( ST \cong UR \), \( \angle RST \cong \angle TUR \)
- Postulate/Theorem: SSS
- Reason: All three sides are congruent.

Final Answer:

\[
\boxed{
\begin{array}{ccc}
1. & \text{SSS} & \\
2. & \text{SAS} & \\
3. & \text{SAS} & \\
4. & \text{ASA} & \\
5. & \text{ASA} & \\
6. & \text{AAS} & \\
7. & \text{SAS} & \\
8. & \text{SSS} & \\
9. & \text{ASA} & \\
10. & \text{AAS} & \\
11. & \text{ASA} & \\
12. & \text{SSS} & \\
\end{array}
}
\]