2.2

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2.2 Analyze Conditional Statements
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Conditional Statement
Hypothesis
Conclusion
Logical statement written in if-then form.
If p, then q.
p?q
Statement following the if
p part
Statement following the then
q part
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True Statement
False Statement
Counterexample
Assuming p is true, the q HAS to happen
Assuming p is true, the q might not happen.
You only need ONE example to prove a statement
false.
One example that proves a statement is false.
When p is true, but q is false.
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Flip the hypothesis and conclusion
Converse
If p, then q becomes If q, then p
q?p
Negate the hypothesis and conclusion
Inverse
If p, then q becomes If not p, then not q
p ? q
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Negate the hypothesis and conclusion of the
converse
Contrapositive
If p, then q becomes If not q, then not p
q ? p
Equivalent to the original statement.
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Biconditional statement
Original and converse of a statement are true.
p if and only if q
p iff q
p ? q AND q ? p
p?q
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1. State the hypothesis and conclusion of the
following
a. If a student studies for a test, then they
will get an A in the class.
conclusion
hypothesis
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1. State the hypothesis and conclusion of the
following
b. If you are a football player, then you are an
athlete.
conclusion
hypothesis
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1. State the hypothesis and conclusion of the
following
c. If x 3, then x2 9.
hypothesis
conclusion
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2. Rewrite the statement in if-then form. Then
write the converse, the inverse, and the
contrapositive.
A car runs when there is gas in the tank.
If a car is running, then there is gas in the
tank.
If-then
If there is gas in the tank, then the car is
running.
Converse
If the car isnt running, then there isnt gas in
the tank.
Inverse
If there isnt gas in the tank, then the car
isnt running.
Contra
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2. Rewrite the statement in if-then form. Then
write the converse, the inverse, and the
contrapositive.
All triangles have three sides.
If a polygon is a triangle, then it has 3 sides.
If-then
If a polygon has 3 sides, then it is a triangle.
Converse
If a polygon isnt a triangle, then it doesnt
have 3 sides.
Inverse
If a polygon doesnt have 3 sides, then it isnt
a triangle.
Contra
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3. Rewrite the definition as a biconditional
statement.
Two angles are complementary angles when the sum
of their measures is 90
Two angles are complementary angles IFF their sum
measures 90
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3. Rewrite the definition as a biconditional
statement.
Equilateral polygons have all of their sides
congruent.
A polygon is equilateral IFF all of the sides are
congruent
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4. Determine if the if-then statement is true or
false. If false, provide a counterexample.
a. If you drive a mustang, then it is red.
False,
You drive a mustang that is black.
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6. Determine if the if-then statement is true or
false. If false, provide a counterexample.
b. If m?2 90, then it is a right angle.
True
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6. Determine if the if-then statement is true or
false. If false, provide a counterexample.
c. If ?A is obtuse, then it measures 155
False,
An obtuse angle that is 100
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6. Determine if the if-then statement is true or
false. If false, provide a counterexample.
d. If you stay after school, then you go to math
tutorial.
False,
You stay after school for sports practice
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7. Decide whether each statement about the
diagram is true. Explain your answer.
m?AEB 90
B
False,
A
C
E
No Box!
D
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7. Decide whether each statement about the
diagram is true. Explain your answer.
AE EC 180
B
False,
A
C
E
Segments arent measured in degrees!
D
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7. Decide whether each statement about the
diagram is true. Explain your answer.
?AED ? ?BEC
B
True,
A
C
E
Vertical Angles
D
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THE FIRE-FISH STORY If there is a fire, then a
fish dies
You are to write a creative story consisting
entirely of conditional statements.
The first statement should
be of the form If there is a fire, then A.
The second
statement should be of the form If A, then B.
The
hypothesis of each statement must be the
conclusion of the previous statement.

The story must be out of at
least 5 conditional statements, ending with If
D, then a fish dies.
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If there is a fire, then _________________________
__________. If ________________, then
If ., then
. If
, then
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx. If
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx, then a fish
dies.
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HW Problem
Section Page Assignment Spiral ?s
2.2 82-85 1-15 odd, 16-18, 19-25 odd Fire-Fish Story 1-6
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An angle measures between 90 and 180 IFF it is
obtuse