1. Write the statement in parentheses as a conditional and provide the truth value (2 points). "An angle that measures 90° is a right angle."
2. Write the statement in parentheses as a converse and provide the truth value (2 points). "An angle that measures 90° is a right angle."
3. Write the statement in parentheses as an inverse and provide the truth value (2 points). "An angle that measures 90° is a right angle."
4. Write the statement in parentheses as a contrapositive and provide the truth value (2 points). "An angle that measures 90° is a right angle."
1. Conditional: If an angle measures 90°, then it is a right angle. (True)
2. Converse: If an angle is a right angle, then it measures 90°. (True)
3. Inverse: If an angle does not measure 90°, then it is not a right angle. (True)
4. Contrapositive: If an angle is not a right angle, then it does not measure 90°. (True)
1. Conditional: If an angle measures 90°, then it is a right angle.
Truth value: True
2. Converse: If an angle is a right angle, then it measures 90°.
Truth value: True
3. Inverse: If an angle does not measure 90°, then it is not a right angle.
Truth value: True
4. Contrapositive: If an angle is not a right angle, then it does not measure 90°.
Truth value: True
1. To write the statement in parentheses as a conditional, we can say: "If an angle measures 90°, then it is a right angle."
To determine the truth value of this conditional statement, we need to examine whether all angles that measure 90° are indeed right angles. Since a right angle by definition measures 90°, the statement is true. The truth value is true.
2. To write the statement in parentheses as a converse, we can say: "If an angle is a right angle, then it measures 90°."
To determine the truth value of this converse statement, we need to examine whether all right angles measure 90°. Since a right angle by definition measures 90°, the statement is true. The truth value is true.
3. To write the statement in parentheses as an inverse, we can say: "If an angle does not measure 90°, then it is not a right angle."
To determine the truth value of this inverse statement, we need to consider whether all angles that do not measure 90° are not right angles. Since there are angles other than 90° that can be right angles (e.g., obtuse right angles), the statement is false. The truth value is false.
4. To write the statement in parentheses as a contrapositive, we can say: "If an angle is not a right angle, then it does not measure 90°."
To determine the truth value of this contrapositive statement, we need to examine whether all angles that are not right angles do not measure 90°. Since there are angles that are not right angles but still measure 90°, such as acute angles, the statement is false. The truth value is false.