In this question, you are asked to identify which statement is a biconditional statement. A biconditional statement is true when both the original statement and its converse are true. It is often written in the form "if and only if," meaning both directions of implication hold: "P if and only if Q" implies "If P then Q" and "If Q then P."

Let's analyze the options:

1. "If an angle is a right angle, then its measure is 90°."
   This is a conditional statement, not biconditional. It only expresses one direction (if right angle, then 90°).

2. "An angle is a right angle if and only if its measure is 90°."
   This is a biconditional statement because it uses the phrase "if and only if," meaning both the original and converse are true. If an angle is a right angle, its measure is 90°, and if an angle's measure is 90°, then it is a right angle.

3. "If an angle’s measure is 90°, then it is not a right angle."
   This is a conditional statement that is false. It is not biconditional.

4. "An angle’s measure is 90° if it is a right angle."
   This is a conditional statement, not biconditional. It only goes in one direction (if right angle, then 90°).

Correct answer:

• The biconditional statement is option 2: "An angle is a right angle if and only if its measure is 90°."

Would you like any further details or explanations?

Related Questions:

1. What is the difference between a conditional and a biconditional statement?
2. Can a statement be true in one direction but false in the converse? Give an example.
3. How do you symbolically represent a biconditional statement in logic?
4. Can a false biconditional statement be converted into a true conditional statement?
5. How do biconditional statements appear in geometric proofs?

Tip:

A biconditional statement can be thought of as defining equivalence between two conditions—if one is true, the other must be true, and vice versa.