geometry statements

A biconditional statement in geometry is a compound statement formed by combining a conditional statement ("If pp, then qq") with its converse ("If qq, then pp") using the phrase "if and only if" (frequently abbreviated as "iff").

Structure and Notation

Symbolically, a biconditional statement is represented as: p⇌qp⇌q or p→q and q→pp→q and q→p

It is expressed in words as "pp if and only if qq".

Truth Conditions

A biconditional statement is true if and only if both constituent statements (pp and qq) share the same truth value—meaning either both are true, or both are false.

Geometric Example

• Conditional (p→qp→q): If an angle is a right angle, then its measure is 90⊤90⊤

• Converse (q→pq→p): If an angle's measure is 90⊤90⊤, then it is a right angle.

• Biconditional (p⇌qp⇌q): An angle is a right angle if and only if its measure is 90⊤90⊤

All precise geometric definitions function as biconditional statements because the definition works logically in both directions.