Which of the following is false for two congruent triangles?

Options

A. Corresponding angles are equal
B. Two sides and included angles are equal
C. Corresponding sides are equal
D. Two angles and one side are equal

Answer

To determine which statement is false for two congruent triangles, we need to analyze the properties of congruent triangles. Congruent triangles are triangles that are identical in shape and size, meaning that all corresponding sides and angles are equal.

### Step-by-Step Solution:

1. **Understanding Congruent Triangles**:
- Congruent triangles have all corresponding sides and angles equal. This means if triangle ABC is congruent to triangle PQR, then:
- \( AB = PQ \)
- \( BC = QR \)
- \( AC = PR \)
- \( \angle A = \angle P \)
- \( \angle B = \angle Q \)
- \( \angle C = \angle R \)

2. **Identifying the Statements**:
- We need to evaluate the given statements about congruent triangles. The statements typically include:
- Corresponding angles are equal.
- Two sides and the included angle are equal (SAS).
- Corresponding sides are equal.
- Two angles and one side are equal (AAS or ASA).

3. **Analyzing Each Statement**:
- **Corresponding angles are equal**: True for congruent triangles.
- **Two sides and the included angle are equal (SAS)**: True for congruent triangles.
- **Corresponding sides are equal**: True for congruent triangles.
- **Two angles and one side are equal**: This is known as the Angle-Angle-Side (AAS) criterion, which is also true. However, if the statement is interpreted as "two angles from any side and their middle side is equal," it can be misleading.

4. **Identifying the False Statement**:
- The statement that is potentially false is the one that suggests an incorrect application of the congruence criteria. Specifically, if it implies that two angles and any side can determine congruence without regard to the position of the angles or side, it would be false.

5. **Conclusion**:
- The false statement is the one that misrepresents the conditions under which triangles can be considered congruent. Therefore, the answer is the option that incorrectly states the criteria for triangle congruence.

### Final Answer:
The false statement regarding congruent triangles is the one that misapplies the congruence criteria, particularly regarding the relationship between angles and sides.