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.