Biconditionals & Definitions. Biconditional Statement Contains the phrase “if & only if” Abbr. iff It is a conditional statement & its converse all in.

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Presentation transcript:

Biconditionals & Definitions

Biconditional Statement Contains the phrase “if & only if” Abbr. iff It is a conditional statement & its converse all in one. Ex: 3 points are collinear iff they are on the same line. Conditional: If 3 pts are collinear, then they are on the same line. Converse: If 3 pts are on the same line, then they are collinear.

A biconditional is true only if the original conditional AND its converse are true!

Ex: Is the statement a biconditional? Is the statement true? x=3 if and only if x 2 =9. Yes, it’s a biconditional. Orig. Conditional statement? If x=3, then x 2 =9. Converse? If x 2 =9, then x=3. True or False? Biconditional is False True False

A conditional statement & its converse can be rewritten as a biconditional only if both statements are true.

Ex: Determine whether the statements are true. If so, rewrite as one biconditional statement. Conditional: If a # ends in 0 or 5, then it is evenly divisible by 5. Converse: If a # is evenly divisible by 5, then it ends in 0 or 5. True or False? Biconditional? A # ends in 0 or 5 iff it is divisible by 5. True True

Definitions can be written in “if- then” form. The converse of a definition is always true. This means the defn. is true forwards & backwards. BICONDITIONAL!!!

Show that the definition of right angle is reversible. Then write it as a biconditional. Definition: A right angle is an angle whose measure is 90.

Adapted from: 0Geometry/Honors%20Geometry%20Power%20Points/2.2%20 Defns%20&%20Biconditionals.ppt