Geo 2.2 ­ Conditional Statements.notebook
Agenda:
Homework:
• Return tests
• #11:PW 2.2 (1-6, 11, 12)
• Return Portfolios
• Due Monday 10/19
October 18, 2015
• Table of Contents
• TC #1 - Sec 2.2: Analyze
Conditional Statements
Big Idea:
How do you write a
biconditional statement?
Homework Quiz:
None today!!!
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Geo 2.2 ­ Conditional Statements.notebook
October 18, 2015
Today we begin the next unit: Chapter 2 - Reasoning and Proof
On your new Table of Contents write the Unit Title, your Name, a Unit Goal, and
Today's Lesson Title and Date.
Reasoning and Proof
(Your Name)
(Your Goal)
Section 2.1: Use Inductive Reasoning
Section 2.2: Analyze Conditional Statements
10/10
10/16
Section 2.3: Law of Syllogism
Now get your practice workbook and tear out all of the chapter 2 pages,
sections 2.1 through 2.7 (p.21-42) and put them in the back of your binder.
Pg. 21 might be in your portfolio - don't worry about it as we will not use
it.
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Geo 2.2 ­ Conditional Statements.notebook
October 18, 2015
2.2 ANALYZE CONDITIONAL STATEMENTS What is a CONDITIONAL STATEMENT?
It is a logical statement that has 2 parts, a hypothesis and a conclusion
It is usually written as an “If‐then” form.
The “If” part represents the hypothesis.
The “then” part represents the conclusion.
Example:
If you study then you will do well.
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Geo 2.2 ­ Conditional Statements.notebook
October 18, 2015
What is a NEGATION of a statement?
It is the opposite of the original statement.
Example 1:
Statement: The ball is red.
Negation: The ball is not red.
Example 2:
Statement: The cat is not black.
Negation: The cat is black.
You write an example now.
Statement:
Negation:
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Geo 2.2 ­ Conditional Statements.notebook
October 18, 2015
How do you write the CONVERSE of a conditional statement?
You exchange the hypothesis and conclusion.
Example:
Statement:
If you study then you will do well.
Converse:
If you did well then you studied.
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Geo 2.2 ­ Conditional Statements.notebook
October 18, 2015
How do you write the INVERSE of a conditional statement?
You negate its hypothesis and conclusion.
Example:
Statement:
If you study then you will do well.
Inverse:
If you did not study then you will not do well.
To negate means the opposite of the statement—use NOT
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Geo 2.2 ­ Conditional Statements.notebook
October 18, 2015
How do you write the CONTRAPOSITIVE of a conditional statement?
You negate the converse.
Example:
Statement:
If you study then you will do well.
Contrapositive:
If you did not do well, then you did not study.
What are equivalent statements?
Statements that are both true or both false.
Note: A conditional statement and its contrapositive are equivalent; they are either both true or both false.
Note: A converse statement and inverse of a conditional statement are equivalent; they are both true or both false.
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Geo 2.2 ­ Conditional Statements.notebook
October 18, 2015
What is a biconditional statement?
When a conditional statement and its converse are both true then the statements can be written as one statement using the form “If and only If”
Conditional Statement:
If 2 lines intersect to form a right angle, then they are perpendicular.
Converse:
If 2 lines are perpendicular, then they intersect to form a right angle.
Since both statements are true we can write a biconditional statement:
2 lines are perpendicular if and only if they intersect to form a right angle.
‐‐‐‐‐ Or‐‐‐‐‐‐ 2 lines intersect to form a right angle if and only if they are perpendicular.
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