Determine whether the conditional and its converse are both true. If both are true, combine them as a biconditional. If either is false, provide a counterexample. If an angle is a right angle, its measure is 90. If an angle measure is 90, the angle is a right angle. One statement is false. If an angle measure is 90, the angle may be an obtuse angle. One statement is false. If an angle is a right angle, its measure may be 180. Both statements are true. The measure of an angle is 90 if and only if it is not a right angle. Both statements are true. An angle is a right angle if and only if its measure is 90.
Both the conditional "If an angle is a right angle, its measure is 90" and its converse "If an angle measure is 90, the angle is a right angle" are true.
We can combine them as a biconditional: "An angle is a right angle if and only if its measure is 90."
The conditional statement is: "If an angle is a right angle, its measure is 90."
The converse statement is: "If an angle measure is 90, the angle is a right angle."
According to the given information, the condition is false, because an angle measure of 90 degrees does not necessarily mean that the angle is a right angle. So, the conditional statement is false.
However, the converse statement is true, because if an angle measure is indeed 90 degrees, then the angle must be a right angle.
Since the conditional and its converse are not both true, we cannot combine them as a biconditional.
In summary:
Conditional statement: False
Converse statement: True
To determine whether the conditional and its converse are both true, we need to analyze each statement separately.
1. Conditional: "If an angle is a right angle, its measure is 90."
- To check if this statement is true, we need to confirm that all right angles have a measure of 90 degrees. This is indeed true, as by definition, a right angle has a measure of 90 degrees.
2. Converse: "If an angle measure is 90, the angle is a right angle."
- To check if this statement is true, we need to verify that all angles with a measure of 90 degrees are right angles. Again, this is true since a right angle is defined as having a measure of 90 degrees.
Since both the original conditional statement and its converse are true, we can combine them as a biconditional.
The biconditional statement would be: "An angle is a right angle if and only if its measure is 90."
This biconditional statement expresses that an angle is a right angle if its measure is 90 and conversely, if an angle is a right angle, its measure is 90.