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The problem asks for the negation of the statement: "If two triangles are congruent, then their areas are equal."

The original statement can be written as:

- **Original Statement**: If two triangles are congruent, then their areas are equal.

To negate this statement, you reverse the implication. The negation would be:

- **Negated Statement**: There exist two congruent triangles whose areas are not equal.

This negation denies the conclusion of the original implication while still accepting the premise.

Would you like more details or have any questions? 

Here are five related questions to expand your understanding:
1. What is the general method for negating conditional statements ("if-then" statements)?
2. Can you provide an example of another conditional statement and its negation?
3. How do congruence and similarity differ in terms of triangle properties?
4. What are the conditions under which two triangles are considered congruent?
5. How does the area formula of a triangle change if we only know the lengths of the sides?

**Tip:** When negating a statement, remember that you are essentially stating that the original condition can be true while the conclusion is false.

Explore how to negate the statement 'If two triangles are congruent, then their areas are equal' in geometry. Learn about triangle congruence theorems and properties, and understand when two congruent triangles may have different areas. Suitable for high school students.

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