Geometry
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Unit 2: Reasoning & Proof
Lesson 2.3:
What are Biconditional Statements and How Can We Use Them?
"A biconditional is a single true statement that combines
a true conditional with its converse."
--Pearson
a true conditional with its converse."
--Pearson
We write biconditionals with the phrase "if and only if."
For example,
"Two angles are supplementary if and only if
the sum of the measures of the two angles is 180º."
This biconditional is made up of the two following statements:
p: Two angles are supplementary.
q: The sum of the measures of two angles is 180º.
For example,
"Two angles are supplementary if and only if
the sum of the measures of the two angles is 180º."
This biconditional is made up of the two following statements:
p: Two angles are supplementary.
q: The sum of the measures of two angles is 180º.
When we have a true biconditional, we can say both of these statements are true:
When you have a true biconditional, you have a good definition.
This is the basis of how we define ideas and objects in our world.
According to Pearson,
This is the basis of how we define ideas and objects in our world.
According to Pearson,
example:
Is this a good definition? "A straight angle is an angle that measures 180."
Good definitions can be written as biconditionals.
We start by defining p and q:
p: An angle is a straight angle.
q: An angle measures 180.