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Geometry CP
Outline Sec. 2-3
Mrs. Sweet
Name:
Date:
Biconditionals and Definitions
Solve It: How would you complete the following sentence? If an animal is an insect, then …?
Explain your reasoning.
A
true
is a single true statement that combines a
and its true
.
You write it using the phrase
of each conditional.
joining the two parts
Writing a Biconditional:
EX. 1: What is the converse of the following true conditional? If the converse is also true, rewrite the
statements as a biconditional.
Conditional: If the sum of the measures of two angles is 90o , then the angles are complementary. .
Converse:
Biconditional:
EX. 2: What is the converse of the following true conditional? If the converse is also true, rewrite the
statements as a biconditional.
Conditional: If two angles have equal measure, then the angles are congruent.
Converse:
Biconditional:
Symbols for a Biconditional Statement: “if and only if”
You can write a biconditional as two conditionals that are
EX 3: What are the two conditionals that form this biconditional?
Two numbers are additive inverses if and only if their sum is 0.
EX. 4: What are two conditionals that form this biconditional?
Two numbers are reciprocals if and only if their product is 1.
Good Definitions:
A good definition is a statement that can help you
an object.

A good definition uses

A good definition is

A good definition is
or
understood terms.
Writing a Definition as a Biconditional:
To determine whether a definition is reversible write the definition as a
the
reversible.
of the conditional. If
and
are true the definition is
EX. 5: Is this definition of an equilateral triangle reversible? If yes, write it as a true biconditional.
An equilateral triangle is a triangle with 3 congruent sides.
EX. 6: Is this definition of a straight angle reversible? If yes, write it as a true biconditional.
A straight angle is an angle that measures 180o
Identifying Good Definitions:
One way to show that a statement is not a good definition is to find a
EX. 7: Which of the following is a good definition:
A. Dogs are animals with 4 paws.
B. Square have 4 sides.
C. Tuesday is the day before Wednesday.
D. An acute angle has a small measure.
EX. 8: Is the following statement a good definition? Explain.
A square is a figure with four right angles.
EX. 9: How can you rewrite the statement “Obtuse angles have greater measures than acute angle” so that it is a
good definition?