Do the following statement and its converse form a biconditional that is true?
If a quadrilateral is square, then it has four right angles.

Let's analyze the statement and its converse to determine if they form a true biconditional.

### Original Statement:
- **If a quadrilateral is square, then it has four right angles.**

This statement is **true** because a square is defined as a quadrilateral with four equal sides and four right angles.

### Converse Statement:
- **If a quadrilateral has four right angles, then it is a square.**

This statement is **false** because a quadrilateral with four right angles could also be a rectangle, which is not necessarily a square (since a rectangle does not need to have four equal sides).

### Biconditional Statement:
- **A quadrilateral is square if and only if it has four right angles.**

This biconditional is **false** because, as shown, the converse does not hold. A quadrilateral having four right angles does not guarantee that it is a square—it could also be a rectangle.

### Conclusion:
The original statement and its converse do not form a true biconditional because the converse is false.

Would you like more details or have any other questions?

Here are 5 related questions for further exploration:
1. What other properties, besides four right angles, define a square?
2. What is the difference between a square and a rectangle in terms of properties?
3. Can a quadrilateral be classified based solely on its angles?
4. What is the converse of other common geometric statements?
5. How does a biconditional statement relate to logical equivalence in geometry?

**Tip:** When checking for a biconditional, ensure that both the original statement and its converse must be true for it to hold.

Explore the concept of biconditional statements in geometry with a focus on a specific example involving squares and quadrilaterals. Learn why the statement 'If a quadrilateral is square, then it has four right angles' forms a true statement, while its converse does not hold. Suitable for students in Grades 9-12.

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