Download 2-1 Conditional Statement

Pre-AP Bellwork
7) The radius of a circle is 4 feet. Describe what
happens to the circle’s area when the radius is
doubled.
Pre-AP Bellwork
8) Use the letters of the alphabet and create
two different sequences that begin with the
same two letters.
Pre-AP Bellwork
9) Draw a Venn Diagram to illustrate the
following conditional statement.
If the game is baseball, then the game is a
team sport.
Pre-AP Bellwork
10) Write the sentence as a conditional
statement: Two complementary angles form a
right angle.
Write the converse, inverse, and contrapositive
of the conditional.
Reasoning and Proof
Chapter 2
2-1 Conditional Statements

What is a conditional statement?

How do you write the converse of a
conditional statement?
2-1Conditional Statements

Conditional

An if – then statement

Two Parts:


Hypothesis – The part following the if
Conclusion – The part following the then
2-1 Conditional Statements
2-1 Conditional Statements
If today is the first day of fall,
then the month is September.
Hypothesis:
Conclusion:
2-1 Conditional Statements
If y – 3 = 5,
then y = 8.
Hypothesis:
Conclusion:
2-1 Conditional Statements

Many sentences can be written as conditionals.
Did you know a
rectangle has four
right angles?
So, you are saying
that if a figure is a
rectangle, then it
has four right
angles?
Can you identify the hypothesis and conclusion?
2-1Conditional Statements
A tiger is an animal.
If something is a tiger, then it is an animal.
2-1 Conditional Statements

Write each sentence as a conditional.

An integer that ends with 0 is divisible by 5.

A square has four congruent sides.

If an integer ends with 0, then it is divisible by 5.

If a figure is a square, then it has 4 congruent
sides.
2-1 Conditional Statements
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Truth Value

True or False

A conditional is proven true if every time the
hypothesis is true, the conclusion is also true.

A conditional only needs 1 counterexample to be
proven false.
2-1 Conditional Statements

Show the conditional is false by finding a
counterexample:

If it is February, then there are only 28 days in the
month.

Since 2008 was a leap year, February had 29
days.
2-1 Conditional Statements

Show the conditional is false by finding a
counterexample:

If the name of a state contains the word New,
then the state borders an ocean.

New Mexico is a state, but it does not border an
ocean.
2-1 Conditional Statement

A Venn diagram can be used to better
understand true conditional statements.

If you live in Chicago, then you live in Illinois.
Illinois
Chicago
2-1 Conditional Statements

Draw a Venn diagram to illustrate this
conditional:

If something is a cocker spaniel, then it is a
dog.
Dog
Cocker
Spaniel
2-1 Conditional Statements

Converse

Switches the hypothesis and conclusion of a
conditional.
Conditional: If two lines intersect to form right
angles, then they are perpendicular.
Converse: If two lines are perpendicular, then they
intersect to form right angles.
2-1 Conditional Statements

Write the converse of the following conditional.
Conditional

If two lines are not parallel and do not intersect, then they
are skew.
Converse

If two lines are skew, then they are not parallel and do not
intersect.
2-1 Conditional Statements

In the last two examples, both the conditional and its
converse are true.

This is not always the case.
Conditional: If a figure is a square, then it has 4 sides.
Converse: If a figure has 4 sides, then it is a square.
This is not true, as any rectangle can be used as a
counterexample.
2-1 Conditional Statements

Write the converse of each conditional
statement. Determine the truth value of the
conditional and its converse.


If two lines do not intersect, then they are parallel.
If two lines are parallel, then they do not intersect.
The conditional is false, but the converse is true.
If x = 2, then |x| = 2.
If |x| = 2, then x = 2.
The conditional is true, but the converse is false.
2-1 Conditional Statements
Conditional Statements and Converses
Statement
Example
Symbolic
Form
You Read It
Conditional
If an angle is a
straight angle,
then its measure
is 180.
p→q
If p, then q.
Converse
If the measure of
an angle is 180,
then it is a straight
angle.
q→p
If q, then p.
2-1 Conditional Statements
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Homework


Pages 72 – 73
33 – 39; 42; 43; 47
5-4 Inverses, Contrapositives,
and Indirect Reasoning

Negation

Opposite truth value

“Knoxville is the capital of Tennessee.”


False
Negation: “Knoxville is not the capital of
Tennessee.”

True
5-4 Inverses, Contrapositives,
and Indirect Reasoning

Write the negation for each statement.




Angle ABC is obtuse.
Angle ABC is not obtuse.
Lines m and n are not perpendicular.
Lines m and n are perpendicular.
5-4 Inverses, Contrapositives,
and Indirect Reasoning

Inverse

Negates the hypothesis and conclusion of a
conditional statement.

Conditional


If a figure is a square, then it is a rectangle.
Inverse

If a figure is not a square, then it is not a rectangle
5-4 Inverses, Contrapositives,
and Indirect Reasoning

Contrapositive

Switches the hypothesis and conclusion
5-4 Inverses, Contrapositives,
and Indirect Reasoning

Conditional


Inverse


If a figure is a square, then it is a rectangle.
If a figure is not a square, then it is not a
rectangle.
Contrapositive

If a figure is not a rectangle, then it is not a
square.
Conditional Statements and Converses
Statement
Example
Symbolic You Read It
Form
p→q
If p, then q.
Conditional
If an angle is a
straight angle,
then its measure
is 180.
Converse
If the measure of
an angle is 180,
then it is a straight
angle.
q→p
If q, then p.
Negation
An angle is not a
straight angle.
~p
Not p.
Inverse
If an angle is not a
straight angle,
then its measure
is not 180.
~p → ~q
If not p, then
not q.
Contrapositive
If an angle’s
measure is not
180, then it is not
a straight angle.
~q → ~p
If not q, then
not p..