Question

write the conditional statement, an angle is a right angle if and only if its measure is 90°, as a conditional and its converse. then determine whether the biconditional is true or false. if it is false, give a counterexample.
conditional
converse
conditional: true or false?
converse: true or false?
if a biconditional is true, then both the conditional and converse are true. if a biconditional is false, then either the conditional or the converse is false or both are false.
biconditional is

Explanation:

A conditional statement is of the form "if p, then q". For the given biconditional "An angle is a right - angle if and only if its measure is 90°", the conditional is "If an angle is a right - angle, then its measure is 90°". The converse is "If the measure of an angle is 90°, then it is a right - angle". By the definition of a right - angle (an angle with measure 90°), the conditional is true because all right - angles have a measure of 90°. The converse is also true because any angle with a measure of 90° is a right - angle. Since both the conditional and the converse are true, the biconditional is true.

Answer:

Conditional: If an angle is a right - angle, then its measure is 90°.
Converse: If the measure of an angle is 90°, then it is a right - angle.
Conditional: true
Converse: true
Biconditional: true