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Lesson 2-3
Conditional Statements
5-Minute Check on Lesson 2-2
Transparency 2-3
Use the following statements to write a compound statement
for each conjunction or disjunction. Then find its truth value.
p: 12 + –4 = 8
q: A right angle measures 90 degrees.
r: A triangle has four sides.
1.
2.
3.
4.
5.
6.
p and r
q or r
~p  r
q  ~r
~p  ~q
Given the following statements, which
compound statement is false?
s: Triangles have three sides.q: 5 + 3 = 8
Standardized Test Practice:
A
sq
B
sq
C
~s  ~q
D
~s  q
5-Minute Check on Lesson 2-2
Transparency 2-3
Use the following statements to write a compound statement for each
conjunction or disjunction. Then find its truth value.
p: 12 + –4 = 8
q: A right angle measures 90 degrees.
r: A triangle has four sides.
12 + –4 = 8 and a triangle has four sides; FALSE
A right angle measures 90 degrees or a triangle has four
sides; TRUE
~p  r
12 + –4  8 or a triangle has four sides; FALSE
q  ~r
A right angle measures 90 degrees and a triangle does not
have four sides; TRUE
~p  ~q
12 + –4  8 or a right angle does not measure 90 degrees;
FALSE
Standardized Test Practice: Given the following statements, which
compound statement is false?
s: Triangles have three sides.q: 5 + 3 = 8
1. p and r
2. q or r
3.
4.
5.
6.
A
sq
B
sq
C
~s  ~q
D
~s  q
Objectives
• Analyze statements in if-then form
• Write the converse, inverse and contrapositive of
if-then statements
Vocabulary
• Implies symbol (→)
• Conditional statement – a statement written in if-then form
• Hypothesis – phrase immediately following the word “if” in
a conditional statement
• Conclusion – phrase immediately following the word “then”
in a conditional statement
• Converse – exchanges the hypothesis and conclusion of
the conditional statement
• Inverse – negates both the hypothesis and conclusion of
the conditional statement
• Contrapositive – negates both the hypothesis and
conclusion of the converse statement
• Logically equivalent – multiple statements with the same
truth values
• Biconditional – conjunction of the conditional and its
converse
If-then Statement:
if <hypothesis - p>, then <conclusion - q>
or p implies q
or in symbols p → q
Related Conditionals:
Example: If two segments have the same measure, then they are congruent
Statement
Conditional
Converse
Hypothesis
p
two segments have the
same measure
Conclusion
q
they are congruent
Formed by
Symbols
Examples
Given hypothesis and
conclusion
p→q
If two segments have the same
measure, then they are congruent
Exchanging the hypothesis and
conclusion of the conditional
q→p
If two segments are congruent, then
they have the same measure
Inverse
Negating both the hypothesis
and conclusion of the
conditional
Contrapositive
Negating both the hypothesis
and conclusion of the converse
~p → ~q
If two segments do not have the
same measure, then they are not
congruent
~q → ~p
If two segments are not congruent,
then they do not have the same
measure
Identify the hypothesis and conclusion of the
following statement.
If a polygon has 6 sides, then it is a hexagon.
If a polygon has 6 sides, then it is a hexagon.
hypothesis
conclusion
Answer: Hypothesis: a polygon has 6 sides
Conclusion: it is a hexagon
Identify the hypothesis and conclusion of the
following statement.
Tamika will advance to the next level of play if she
completes the maze in her computer game.
Answer: Hypothesis: Tamika completes the maze in her
computer game
Conclusion: she will advance to the next level
of play
Determine the truth value of the following statements
for each set of conditions.
If it rains today, then Michael will not go skiing.
a. It does not rain today; Michael does not go skiing.
Answer: true
b. It rains today; Michael does not go skiing.
Answer: true
c. It snows today; Michael does not go skiing.
Answer: true
d. It rains today; Michael goes skiing.
Answer: false
Write the converse, inverse, and contrapositive of the
statement All squares are rectangles.
Determine whether each statement is true or false.
If a statement is false, give a counterexample.
First, write the conditional in if-then form.
Conditional: If a shape is a square, then it is a rectangle.
The conditional statement is true.
Write the converse by switching the hypothesis and
conclusion of the conditional.
Converse: If a shape is a rectangle, then it is a square.
The converse is false. A rectangle with ℓ = 2
and w = 4 is not a square.
Inverse:
If a shape is not a square, then it is not a
rectangle. The inverse is false. A 4-sided
polygon with side lengths 2, 2, 4, and 4 is
not a square, but it is a rectangle.
The contrapositive is the negation of the hypothesis and
conclusion of the converse.
Contrapositive: If a shape is not a rectangle, then it is
not a square. The contrapositive is true.
Write the converse, inverse, and contrapositive of the
statement The sum of the measures of two
complementary angles is 90.
Determine whether each statement is true or false.
If a statement is false, give a counterexample.
Answer:
Conditional: If two angles are complementary, then the sum of
their measures is 90; true.
Converse: If the sum of the measures of two angles is 90,
then they are complementary; true.
Inverse: If two angles are not complementary, then the sum of
their measures is not 90; true.
Contrapositive: If the sum of the measures of two angles is not
90, then they are not complementary; true.
Conditional
If two lines are perpendicular, then their angle is right.
Converse
Inverse
Contrapositive
Conditional
Converse
If two angles are supplementary, then they sum to 180º
Inverse
Contrapositive
Conditional
Converse
Inverse
If today is not Friday, then we do not have a quiz.
Contrapositive
Conditional
Converse
Inverse
Contrapositive If two angles aren’t a linear pair, then they aren’t supplementary.
Conditionals in Symbols
Statements
Conditional
Converse
Inverse
Contrapositive
Symbology
P →Q
Q→P
~P →~Q
~Q→~P
Summary & Homework
• Summary:
– Conditional statements are written in if-then form
– Form the converse, inverse and contrapositive of an
if-then statement by using negations and by
exchanging the hypothesis and conclusion
• Homework:
Day 1: pg 78, 5, 6, 8, 9, 13, 17, 21, 23, 25, 27
Day 2: pg 79-81, 43, 45, 53, 55, 57, (pg 81 1, 3)