Question

write the biconditional as a conditional and its converse. then determine whether the biconditional is true or false. an angle is acute if and only if it has a measure less than 90°. conditional: if select choice then select choice converse: if an angle measures less than 90°, then it is select choice the conditional and the converse are select choice so the biconditional is select choice

Explanation:

Step1: Write the conditional statement

A conditional statement is of the form "if p then q". For the biconditional "An angle is acute if and only if it has a measure less than 90°", the conditional is: If an angle is acute, then it has a measure less than 90°.

Step2: Write the converse statement

The converse of "if p then q" is "if q then p". So the converse is: If an angle has a measure less than 90°, then it is acute.

Step3: Determine truth - values

By definition, an acute angle is an angle whose measure is less than 90°. So the conditional "If an angle is acute, then it has a measure less than 90°" is true. Also, if an angle has a measure less than 90°, by the definition of an acute angle, it is acute. So the converse is true. Since both the conditional and the converse are true, the biconditional is true.

Answer:

Conditional: If an angle is acute, then it has a measure less than 90°.
Converse: If an angle has a measure less than 90°, then it is acute.
The conditional and the converse are true, so the biconditional is true.