This document summarizes key concepts about conditional statements, including: - Conditional statements have two parts - a hypothesis and a conclusion connected by "if-then". They can be either true or false. - The converse of a conditional statement switches the hypothesis and conclusion. - A biconditional statement means both the original statement and its converse are true. - Examples are provided of conditional statements that are true, false, and their converses. Counterexamples are used to show statements that are false.

1. Ch3.6_ConditionalStatementsLogic.notebook October 04, 2011
Is this Possible?
It has been reported
that on any day, 8%
of the American population
eats at McDonald's
Assume the Assume there are
population is 12,800 restaurants
310 million
Chapter 3.6
Conditional Statements
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2. Ch3.6_ConditionalStatementsLogic.notebook October 04, 2011
Conditional Statements
("If­Then" Statements)
Are either
Have 2 parts True or False
If [HYPOTHESIS], then [CONCLUSION]
If it is raining, then the ground is wet.
TRUE FALSE
If it is Wednesday, then there is no
homeroom.
TRUE FALSE
If a statement is false,
we need a counterexample
If a number is divisible by 2, then it
is also divisible by 4.
TRUE FALSE
If line t intersects lines g and h, then
line t is a transversal
TRUE FALSE
If 2 lines do not intersect, then they
are parallel
TRUE FALSE
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3. Ch3.6_ConditionalStatementsLogic.notebook October 04, 2011
In General
If p then q
If it is raining, then the ground is wet.
Converse
If q then p
If the ground is wet, then it is raining.
Biconditional
Statements
Both the statement and its
converse are true
If p then q
AND If and only if
If q then p ("iff")
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4. Ch3.6_ConditionalStatementsLogic.notebook October 04, 2011
Biconditional
Statements
If an angle measure is 900,
then it is a right angle TRUE
If an angle is a right angle,
then its measure is 900 TRUE
An angle is a right angle if
and only if its measure is 900
Write the converse of this statement:
If two angles are vertical angles,
then they have the same measure
TRUE or FALSE
CONVERSE:
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5. Ch3.6_ConditionalStatementsLogic.notebook October 04, 2011
Each of the following statements is false.
Think of a counterexample for each statement.
If PQ = QR, then the point Q is the midpoint of PR
If points A, B, and C are collinear, then
BA and BC are opposite rays
If two angles share a common side and vertex,
then they are adjacent angles.
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