2.3 biconditionals .notebook
September 21, 2016
9/21/16 ‐ Warm Up Problem
Write the converse of each statement.
1. If an angle is 90 degrees, then it is a right angle.
2. If two angles are vertical, then they are congruent.
Sep 20­10:03 AM
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2.3 biconditionals .notebook
September 21, 2016
Section 2.3 - Biconditionals Statements
Goals: Recognize and write biconditional statements
Biconditional: can be written when a conditional statement and its converse are both true
­ the hypothesis and conclusion are joined together with the words "if and only if"
Example:
Conditional: If two angle add to 180 degrees, then they are supplementary.
Converse:
If they are supplementary, then two angles add to 180 degrees.
Biconditional:
Two angles add up to 180 degrees if and only if they are supplementary.
The point of a biconditional is to let the reader know that
the statement is true no matter what order the parts are in.
Sep 20­10:07 AM
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2.3 biconditionals .notebook
September 21, 2016
In your notes...
Write the converse of the statement below. If it is
true, write a biconditional statement.
Conditional: If two angles have the same measure, then the angles are congruent.
Converse:
If two angles are congruent, then they have the same measure.
Biconditional:
Two angles are congruent if and only if they have the same measure.
Sep 24­1:59 PM
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2.3 biconditionals .notebook
September 21, 2016
Could we write these statements as biconditionals?
What would the biconditional be?
If today is Tuesday, then tomorrow is Wednesday.
Today is Tuesday if and only if tomorrow is Wednesday.
If two angles are a linear pair, then they are
supplementary.
No biconditional. Converse is not true.
If 3 points are collinear, then they lie on the same
line.
Three points are collinear if and only if they lie on the same
line.
Sep 20­10:16 AM
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2.3 biconditionals .notebook
September 21, 2016
Sep 20­10:30 AM
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2.3 biconditionals .notebook
September 21, 2016
Good Definition:
- uses already understood terms
- is precise
- can be written as a biconditional
Is each a good definition? Could you write it as a
biconditional?
A cat is a mammal with whiskers and a tail.
An airplane is a vehicle that flies.
A right angle is an angle whose measure is 90.
Sep 20­10:35 AM
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2.3 biconditionals .notebook
September 21, 2016
Assignment:
2.2-2.3 Worksheet
(back)
Sep 18­2:14 PM
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