Geometry
Notes 2-4: Biconditional Statements and Definitions
Ch. 2: Geometric Reasoning
1) Biconditional Statement: a combination of a ____________________ statement and its _________________.
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This means “If ____, then ____.” & “If ____, then ____.” Or “p _____ ______ ________ ____ q” (____)
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We can write it in math as: _______________, which means __________ & __________.
EX 1: Given the biconditional statement, underline the hypothesis, circle the conclusion, then write the
conditional and the converse.
An angle is acute if and only if its measurement is between 0o and 90o.
p  q : ____________________________________________________________________________________
q  p : ____________________________________________________________________________________
EX 2: Given the hypothesis and conclusion, write a biconditional statement.
p : 5 x  8  37
q:x 9
p  q : ____________________________________________________________________________________
3) For a biconditional statement to be true, both the conditional statement and its converse must be __________.
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If either is false, then the biconditional statement is __________.
EX 3: Find the truth value of the conditional and converse. Is the biconditional statement is true or false?
Conditional: If the dimensions of a rectangle are 12 in. by 4 in., then the rectangle’s area is 48 in. 2. _____
Converse: If a rectangle’s area is 48 in. 2, then the dimensions of the rectangle are 12 in. by 4 in.
_____
Biconditional: The dimensions of a rectangle are 12 in. by 4 in. if and only if its area is 48 in. 2.
_____
4) In Geometry, biconditional statements are used to write _________________________.
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Think of definitions as being reversible. _______________, however, are not always true when reversed.
5) Polygon: a _______________, plane figure formed by _____ or more segments.
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Which are not polygons?
EX 4: Write the definition as a biconditional statement.
Definition: A pentagon is a 5-sided polygon.
Biconditional: _________________________________________________________________________