2-3 Biconditionals and Defintions. Biconditional- a statement that is the combination of a conditional statement and its converse. If the truth value.

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Presentation transcript:

2-3 Biconditionals and Defintions

Biconditional- a statement that is the combination of a conditional statement and its converse. If the truth value of both the conditional and converse are true then we can write a biconditional

Conditional: If two angles have the same measure, then the angles are congruent TRUTH VALUE: Converse: If two angles are congruent, then they have the same measure TRUTH VALUE: TRUE

BICONDITIONAL: Two angles have the same measure if and only if the angles are congruent. BOTH the conditional and converse are true….. So I can write a BICONDITIONAL To write a biconditional always use if and only if

OYO… Given the conditional. Find the truth value of the conditional and its converse, then write a biconditional Conditional: If three points are collinear, then they lie on the same line TRUTH VALUE: Converse: TRUTH VALUE: BICONDITIONAL: Three points are collinear if and only if they lie on the same line TRUE If three points lie on the same line, then they are collinear

A biconditional combines p q and q p, so we write a biconditional in the symbolic form: p q

Writing a definition as a Biconditional Definition- Perpendicular lines are two lines that intersect to form right angles. Conditional- Truth Value- Converse- Truth Value- Biconditional- TRUE If two lines are perpendicular, then they intersect to form right angles If two lines intersect to form right angles, then they are perpendicular. TRUE Two lines are perpendicular if and only if they intersect to form right angles

Think. Pass. Solve Write down a conditional (involving geometry) that would prove true. Pass the conditional to the person behind you. Write the converse of the conditional. Find the truth value of the converse. Pass again. Write the biconditional if both the conditional and converse were true.