Transcript Conditional Statements

Conditional Statements
SECTION 2.1
Learning Outcomes
 I will be able to write conditional statements in if-
then form.
 I will be able to label parts of a conditional
statement.
 I will be able to write the converse, inverse and
contrapositive of a conditional statement.
Vocabulary
 A conditional statement is a type of logical statement
that has two parts, a hypothesis and a conclusion.
 If-then form of a conditional statement uses the
words “if” and “then.”
 Example: If today is Friday, then tomorrow is
Saturday.
Parts of a Conditional Statement
 A hypothesis is the “if” part of a conditional
statement.
 A conclusion is the “then” part of a conditional
statement.
 In our example:
 If today is Friday, then tomorrow is Saturday.
Think-Pair-Share
 Write the statement as a conditional statement in if-
then form.
 All students taking geometry have math during an
even numbered block.
If students are taking Geometry, then they
have math during an even numbered block.
Converse
 The converse of a conditional statement is formed by
switching the hypothesis and the conclusion.
 From our example: If today is Friday, then
tomorrow is Saturday.
 The converse would be: If tomorrow is Saturday,
then today is Friday.
Inverse
 An inverse is the statement formed when you negate
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the hypothesis and conclusion of a conditional
statement.
What is a negation?
The negation of a statement is formed by writing the
negative of the statement.
In our example: If today is Friday, then tomorrow is
Saturday.
The inverse would be: If today is not Friday, then
tomorrow is not Saturday.
Contrapositive
 A contrapositive is the statement formed when you
negate the hypothesis and conclusion of the converse
of a conditional statement.
 In our example: If today is Friday, then tomorrow is
Saturday.
 The contrapositive would be: If tomorrow is not
Saturday, then today is not Friday.
In Review
 Original Statement: If today is Friday, then
tomorrow is Saturday
 Converse: If tomorrow is Saturday, then today is
Friday
 Inverse: If today is not Friday, then tomorrow is not
Saturday.
 Contrapositive: If tomorrow is not Saturday, then
today is not Friday.
Random Postulates
Review
 Write the converse of this statement
 I will go to the game if I get all of my homework
done.
Converse: If I go to the game, then I got all of my
homework done.
Review
 Write the inverse of this statement:
 I will go to the game if I get all of my homework
done.
Inverse: If I do not get all my homework done, then I will
not go to the game
Review
 Write the contrapositive of this statement:
 I will go to the game if I get all of my homework
done.
Contrapositive: If I do not go to the game, then I did not get
all my homework done.
Biconditionals and Laws
SECTION 2.2
Outcomes
 I will be able to write biconditional statements if the
properties for a biconditional statement exist
Biconditional Statements
 A biconditional statement is a statement that
contains the phrase “if and only if.”
 For a biconditional statement to be true, you must:
 Verify that the conditional statement is true.
 Verify that the converse of the statement is true.
Rewriting Biconditional Statements
 Rewrite the biconditional statement as a statement and
its converse.
 Two angles are congruent if and only if they have the
same measure.
If two angles have the same measure, then they are
congruent.
Converse:If two angles are congruent, then
they have the same measure.
Evaluating Biconditional statements
 Is the following biconditional statement true?
 Two angles are congruent if and only if they have
the same measure.
If two angles have the same measure, then they are
congruent.
Converse:If two angles are congruent, then
they have the same measure.
Evaluate the biconditional statement to see if it
is true.
 x = 4 if and only if x2 = 16.
If x = 4, then x2 = 16 
If x2 = 16, then x = 4.

Can the statement be written as a biconditional?
 Example: If you are 15 years old, then you are a
teenager.
 First, evaluate the statement. Is it true?
 Second, write the converse of the statement.
 Third, evaluate the converse. Is it true?
 Converse: If you are a teenager, then you are 15
years old. 
Definitions
 Two lines are perpendicular lines if they intersect
to form a right angle.
Definitions
 A line perpendicular to a plane is a line that
intersects the plane in a point and is perpendicular
to every line in the plane that intersects it.
Exit Ticket
Homework
 Pg. 75: 22-24, 44-49
 Pg. 83: 13-23, 32-35