Biconditional statements do not use the key words 'if' and 'then.' Biconditional statements are true statements that combine the hypothesis and the conclusion with the key words 'if and only if.'
For example, the statement will take this form: (hypothesis) if and only if (conclusion). We could also write it this way: (conclusion) if and only if (hypothesis). If you figured out that both the conditional and converse statements have to be true for a biconditional statement to exist in geometry, you are correct. It's like a reversible jacket; you can wear it on both sides.
Let's rewrite our last example:
Conditional statement: If a polygon has three sides, then it is a triangle.
Converse statement: If a polygon is a triangle, then it has three sides.
Since both are statements are true, we can go ahead and make our biconditional statements:
A polygon is a triangle 'if and only if' it has three sides.
A polygon has three sides 'if and only if' it is a triangle.
Since we can write two biconditional statements, we could also define them as compound statements, since both the conditional and the converse statements have to be true. Let's practice some more.
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