Two triangles are congruent if three angles of one triangle are equal to three angles of the other triangle.

Answer

To determine whether the statement "Two triangles are congruent if three angles of one triangle are equal to three angles of the other triangle" is true or false, we can analyze the properties of triangles and congruence.

### Step-by-Step Solution:

1. **Understanding Congruence**:
- Two triangles are said to be congruent if they are identical in shape and size. This means that all corresponding sides and angles must be equal.

2. **Analyzing the Given Condition**:
- The statement claims that if the three angles of one triangle are equal to the three angles of another triangle, then the triangles are congruent.

3. **Considering Examples**:
- Let's take two triangles, Triangle A and Triangle B. Assume both triangles have angles measuring 60°, 60°, and 60°.
- Triangle A could be a small equilateral triangle, while Triangle B could be a larger equilateral triangle.

4. **Comparing the Triangles**:
- Both triangles have the same angles (60° each), which means they are similar triangles. However, they are not congruent because their side lengths are different.

5. **Conclusion**:
- Since we have established that two triangles can have the same angles but different side lengths, we conclude that the statement is false. For two triangles to be congruent, not only must their angles be equal, but their corresponding sides must also be equal.

6. **Justification**:
- The justification for this conclusion is based on the properties of triangles. The congruence rules (such as SSS, SAS, ASA, and RHS) do not include a rule for AAA (Angle-Angle-Angle), which means that having equal angles alone does not guarantee congruence.

### Final Answer:
The statement is **false**. Two triangles are not necessarily congruent if their angles are equal; their sides must also be equal.

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