SB Geom 2­2 Completed.notebook
September 11, 2012
Lesson 2.2 Analyze Conditional Statements
Remember when your mom would say, if you do this... then ....
conditional statement ­ a logical statement that has two parts, a hypothesis and a conclusion
if­then form ­ a conditional statement with an if and a then
hypothesis ­ the "if" part of a conditional statement
conclusion ­ the "then" part of a conditional statement
What is the hypothesis and the conclusion?
If it is raining, then there are clouds in the sky.
Sep 3­7:48 AM
Expl 1. Rewrite the conditional statement in if­then form.
a. All birds have feathers.
b. Two angles are supplementary if they are a linear pair.
Rewrite the conditional statement in if­then form.
1. All 90o angles are right angles. 2. 2x + 7 = 1, because x = ­3.
3. When n = 9, n 2 = 81. 4. Tourists at the Alamo are in Texas.
Sep 3­7:52 AM
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SB Geom 2­2 Completed.notebook
September 11, 2012
negation ­ the opposite of the original statement ( NOT )
The ball is red.The cat is not black.
Converse ­ a conditional statement with the hypothesis and converse switched
Inverse ­ a conditional statement with negation of hypothesis and converse
Contrapositive ­ a conditional statement with the hypothesis and converse switched and negated
Conditional statement: If x = 2, then x + 3 = 5.
Converse:
Inverse:
Contrapositive:
Sep 3­7:58 AM
Expl 2. Write the if­then form, converse, inverse, and contrapositive of "Guitar players are musicians." Decide whether each is true or false.
If­then:
Converse:
Inverse:
Contrapositive:
Write the converse, inverse, and contrapositive of each statement. Tell whether each is true or false.
5. If a dog is a Great Dane, then it is large.
6. If a polygon is equilateral, then the polygon is regular.
Sep 3­8:15 AM
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SB Geom 2­2 Completed.notebook
September 11, 2012
equivalent statements ­ two statements are both true or false
­ conditional statement and contrapositive
­ converse and inverse
perpendicular lines ­ two lines that intersect to form a right angle
T
­ the symbol for perpendicular is Expl 3. Decide whether each statement about the diagram is true.
T
a. AC BD
b. <AEB and <CEB are a linear pair
c. EA and EB are opposite rays
Sep 3­8:18 AM
Decide whether each statement is true. Explain your answer using the definitions you have learned.
7. <JMF and <FMG are supplementary.
8. Point M is the midpoint of FH.
9. <JMF and <HMG are vertical angles.
10. FH JG
T
Sep 3­8:26 AM
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SB Geom 2­2 Completed.notebook
September 11, 2012
Biconditional statement ­ a statement that contains the phrase
"if and only if"
Expl 4. Write the definition of perpendicular lines as a biconditional. 11. Rewrite the definition of right angle as a biconditional statement.
12. Rewrite the statement as a biconditional.
If Mary is in theater class, she will be in the fall play. If Mary is in the fall play, she must be taking theater class.
Sep 3­8:30 AM
Homework
Lesson 2-2
1-25
Sep 3­8:34 AM
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