2-3 Biconditionals and Definitions
Biconditional
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A _______________ is a single true statement that combines a true _______________ and its true
_______________.
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Use the phrase _____ _______ _______ _____.
Writing a Biconditional
Problem 1
What is the converse of the following true conditional? If the converse is also true, rewrite the statements as
a biconditional.
a) If the sum of the measures of two angles is 180, then the two angles are supplementary.
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b) If two angles have equal measure, then the angles are congruent.
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Biconditional Statements
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A biconditional combines __________ and __________ as __________.
Identifying the Conditionals in a Biconditional
Problem 2
What are the two conditional statements that form this biconditional?
a) A ray is an angle bisector if and only if it divides an angles in two congruent angles.
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b) Two numbers are reciprocals if and only if their product is 1.
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Writing a Definition as a Biconditional
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A good definition is a statement that can help you _______________ or classify an _______________.
o Use _______________ understood terms
o Be _______________.
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Avoid words such as _______________, _______________, _______________, or
_______________.
o Make sure it’s _______________.
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A _______________ biconditional.
Problem 3
Is this definition reversible? If yes, write it as a true biconditional.
a) A quadrilateral is a polygon with four sides.
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b) A straight angle is an angle that measures 180.
c) An equilateral triangle is a triangle with 3
congruent sides.
Identifying Good Definitions
Problem 4
Which of the following is a good definition?
a) A fish is an animal that swims.
d) A penny is a coin worth one cent.
b) Rectangles has four corners.
e) A square is a figure with 4 right angles.
c) Giraffes are animals with very long necks.
f) Obtuse angles have greater measures
than acute angles.