DEFINITIONS AND BICONDITIONAL STATEMENTS Section 2 2 Definitions
DEFINITIONS AND BICONDITIONAL STATEMENTS Section 2. 2
Definitions •
Biconditionals • Biconditional: a statement that contains the phrase “if and only if” (iff). It is like writing a statement and its converse. • Example: 3 points are collinear if and only if they lie on the same line. • If 3 points are collinear, then they lie on the same line. • If 3 points lie on the same line, then they are collinear. • Rewrite the biconditional statement as a conditional statement and its converse. • A point is a midpoint of a segment if and only if it divides the segment into two congruent segments.
Analyzing Biconditionals • Determine whether the biconditional staements is true or false. If false, provide a counterexample. • You live in Idaho if and only if you live in the United States. • 2 angles form a linear pair if and only if the 2 angles are supplementary. • 2 angles are complementary if and only if the sum of their measures if 90 degrees.
Rewriting Statements • Rewrite the true statement in if-then form and write the converse. If the converse is true, combine it with the ifthen statement to form a true biconditional statement. If the converse is false, provide a counterexample. • Two circles have the same circumference if they have the same diameter. • All leopards have spots.
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