S E C T I O N 2 . 1

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I will be able to write conditional statements in ifthen 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.

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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.

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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.

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Write the statement as a conditional statement in ifthen form.
All students taking geometry have math during an even numbered block.

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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.

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An inverse is the statement formed when you negate 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.

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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.

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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.

 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.

 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

 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.

S E C T I O N 2 . 2

 I will be able to write biconditional statements if the properties for a biconditional statement exist

 A biconditional statement is a statement that contains the phrase “if and only if.”
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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.

 Rewrite the biconditional statement as a statement and its converse.
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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.

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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 x 2 = 16.
If x = 4, then x 2 = 16 
If x 2 = 16, then x = 4. 

Can the statement be written as a biconditional?
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Example: If you are 15 years old, then you are a teenager.
First, evaluate the statement. Is it true?
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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. 

 Two lines are perpendicular lines if they intersect to form a right angle.

 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.

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Pg. 75: 22-24, 44-49
Pg. 83: 13-23, 32-35