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Biconditional statements

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When a conditional and its converse are both true, we call this a biconditional. A biconditional means that the hypothesis is true if and only if the conclusion is true. [Some math teachers like to abbreviate ‘if and only if’ as ‘iff’.]

It is also appropriate to call a biconditional statement a definition, because it says the hypothesis and the conclusion imply each other (so they are the same thing).

Here’s an example of a biconditional:

Conditional:  If an angle is a right angle, then it has a measure of 90°.

Converse: If an angle has a measure of 90°, then it is a right angle.

Both of these statements are true, and so we could also call this a definition: A right angle is an angle with a measure of 90°.

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