Download 2.2 CP Conditional Statements.notebook

2.2 CP Conditional Statements.notebook
September 21, 2016
Do Now #12
Find the next object in the pattern.
1.
2. alligator, banana, cactus, __________
3. Fall, winter, spring, __________
4. 1, 4, 9, 16, ______
What we will learn today:
• Analyze the truth value of a conditional
statement,
• Write the inverse, converse, and
contrapositive of a conditional
statement
Often times in advertising we hear...
“If you are not 100% satisfied with this
product, then return it for a full refund of
the purchase price.”
Conditional statements have two parts.
• The hypothesis (p) is the part following the if.
• The conclusion (q) is the part following the then.
Examples ~ Write each conditional statement
if-then form.
(1) Two angles are congruent if they have the
same measures.
in
(2) We will cancel practice if it rains tonight.
(3) Points that lie on the same line are collinear.
(4) Two angles that are complementary are acute.
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2.2 CP Conditional Statements.notebook
September 21, 2016
Writing the converse of a conditional statement
Original statement: p --> q
Converse: q --> p
The converse of a conditional statement is formed by
exchanging the hypothesis and conclusion of a
conditional.
Conditional: If a figure is a triangle, then it has three angles
Hypothesis:
Conclusion:
Converse: If ____________________, then _________________.
Conditional: If it isn't raining , then I will walk home
Hypothesis:
Conclusion:
Converse: If ____________________, then _________________.
Conditional: If the Tigers win , then Ms. Gaddis is happy
Hypothesis:
Conclusion:
Converse: If ____________________, then _________________.
Conditional: If two planes intersect, then a line is formed
Hypothesis:
Conclusion:
Converse: If ____________________, then _________________.
The converse, inverse, and contrapositive of
a conditional statement
Original If-Then statement:
Converse :
Inverse:
Contrapositive:
Examples
(1) p --> q: If two angles are vertical angles, then
they are congruent.
converse (q --> p):
inverse (~p --> ~q):
contrapositive (~q --> ~p):
(2) If two angles are complementary, then the
sum of their measures is 90o .
converse:
inverse:
contrapositive:
(3) If points are coplanar, then they lie in the
same plane.
converse:
inverse:
contrapositive:
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2.2 CP Conditional Statements.notebook
September 21, 2016
When you combine a conditional statement and its
converse, you create a biconditional statement.
“p if and only if q.” = “if p, then q”
and
“if q, then p”
p q means p q and q p
Example 1 ~ Write the conditional statement and
converse within the biconditional.
(1) An angle is obtuse if and only if its measure is
greater than 90° and less than 180°.
p: its measure is greater than 90 o and less
than 180 o
q: the angle is obtuse
p --> q: If an angles measure is greater than 90o &
less than 180 o , then the angle is obtuse.
q --> p: If an angle is obtuse, then its measure
is greater than 90 o and less than 180 o
In Geometry, biconditional statements
are used to write definitions.
In the glossary, a polygon is
defined as a closed plane figure
formed by three or more line
segments.
Example 4 ~ Write each definition as a biconditional
statement.
(a) A pentagon is a five-sided polygon.
(b) A triangle is a three-sided polygon.
(c) Perpendicular lines form four right angles.
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2.2 CP Conditional Statements.notebook
September 21, 2016
txt.pg.75 #7, 10, 12, 13, 19­21
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