SOLUTION: 3.) A polygon can be regular if and only if the sides are congruent. (“if and only if” states a condition but does not necessitate it to be the sole condition) true or false?
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Question 391392: 3.) A polygon can be regular if and only if the sides are congruent. (“if and only if” states a condition but does not necessitate it to be the sole condition) true or false?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
"A polygon can be regular if and only if the sides are congruent." True statement, but not strong enough.
"A polygon is regular if and only if the sides are congruent."
is the proper way to make the statement.
On the other hand it is also true that a polygon is regular if and only if the interior angles are congruent. The thing is, it can also be said that the angles of a polygon are congruent if and only if the sides are congruent. Hence, I don't see how your original statement illustrates the idea that an "if and only if" condition is not necessarily the sole condition.
"If and only if" indicates a condition that is both necessary and sufficient for the truth of the premise.
John
My calculator said it, I believe it, that settles it
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