The circumcentre of a triangle occurs at the midpoint of the hypotenuse if and only if the triangle is a right triangle.

The biconditional sentence above compactly states the following four conditional sentences:

• if the circumcentre of a triangle occurs at the midpoint of the hypotenuse, then the triangle is a right triangle.
• if a triangle is a right triangle, then the circumcentre of the triangle occurs at the midpoint of the hypotenuse.
• if the circumcentre of a triangle DOES NOT occur at the midpoint of the hypotenuse, then the triangle is NOT a right triangle.
• if a triangle is NOT a right triangle, then the circumcentre of the triangle DOES NOT occur at the midpoint of the hypotenuse.

If "P" represents one statement and "Q" represents another statement, then "If P then Q" is called a conditional sentence symbolized as "P → Q"

The following four conditional sentences can be considered:

The biconditional sentence P if and only if Q states that the conditional sentence, its converse, inverse and contrapositive are all true.

The biconditional sentence of this example can be broken up into the two parts below.

P: the circumcentre of a triangle occurs at the midpoint of the hypotenuse

Q: the triangle is a right triangle

P if and only if Q [i.e. P ↔ Q] results in the following:

• (Conditional sentence: "If P then Q" [P → Q]) if the circumcentre of a triangle occurs at the midpoint of the hypotenuse, then the triangle is a right triangle.
• (Converse: "If Q then P" [P ← Q]) if a triangle is a right triangle, then the circumcentre of the triangle occurs at the midpoint of the hypotenuse.
• (Inverse: "If ~P then ~Q" [~P → ~Q]) if the circumcentre of a triangle DOES NOT occur at the midpoint of the hypotenuse, then the triangle is NOT a right triangle.
• (Contrapositive: "If ~Q then ~P" [~P ← ~Q]) if a triangle is NOT a right triangle, then the circumcentre of the triangle DOES NOT occur at the midpoint of the hypotenuse.