Day 1: Logical Reasoning Unit 2. Updates & Reminders Check your grades on pinnacle Exam corrections...

Day 1: Logical Reasoning

Unit 2

Updates & RemindersCheck your grades on pinnacleExam corrections due tomorrowVocab Quiz Friday

Warm Up Warm Up & & JournalJournal

Describe in your own words how to construct a congruent angle.

Assignment SheetDatDatee

AssignmentAssignment GradGradee

SignaturSignaturee

1-24 Textbook Assignment Page 716 & 732 ____/20

1-27 Unit 2 Vocabulary

1-27 Unit 2 Book Outline ____/10

1-28 Notes on Logic Statements

1-28 Gap Day Wkst #1

1-28 Gap Day Wkst #2

1-28 Logic Statement HW #1 ____/5

Example 1 Identify the Hypothesis and Conclusion

Identify the hypothesis and the conclusion of the if-then statement.

If I pass the driving test, then I will get my driver’s license.

SOLUTION

I pass the driving test is the hypothesis.

I will get my driver’s license is the conclusion.

Example 2 Write If-Then Statements

Rewrite the statement as an if-then statement.

a. Every game on my computer is fun to play.

I will buy the CD if it costs less than $15.

b.

SOLUTION

a. If a game is on my computer, then it is fun to play.

If the CD costs less than $15, then I will buy it.b.

Example 3 Use the Law of Detachment

What can you conclude from the following true statements?

If you wash the cotton T-shirt in hot water, then it will shrink.

You wash the cotton T-shirt in hot water.

SOLUTION

The hypothesis (you wash the cotton T-shirt in hot water) of a true if-then statement is true. By the Law of Detachment, the conclusion must be true.

ANSWERYou can conclude that the cotton T-shirt shrinks.

Checkpoint If-Then Statements and the Law of Detachment

Rewrite the statement as an if-then statement. Then underline the hypothesis and circle the conclusion.

All teachers at East High School have taught for at least 5 years.

1.

An angle is obtuse if its measure is 170°.2.

ANSWER If a teacher works at East High School, then

he or she has taught for at least 5 years.

ANSWER If the measure of an angle is 170°, then

the angle is obtuse.

Checkpoint If-Then Statements and the Law of Detachment

What can you conclude from the given true statements?

If x has a value of 7, then 2x – 3 has a value of 11. The value of x is 7.

3.

If you study at least two hours for the test, then you will pass the test. You study three hours for the test.

4.

ANSWER 2x – 3 has a value of 11.

ANSWER You will pass the test.

Example 4 Use the Law of Detachment

Which argument is correct? Explain your reasoning.If two angles are vertical angles, then they are congruent. 1 and 2 are congruent.

So, 1 and 2 are vertical angles.

Argument 1:

If two angles are vertical angles, then they are congruent. 1 and 2 are vertical angles. So, 1 and 2 are congruent.

Argument 2:

SOLUTION

Argument 2 is correct. The hypothesis (two angles are vertical angles) is true, which implies that the conclusion

(they are congruent) is true.

You can use the following counterexample to show that Argument 1 is false. In the diagram at

the right, 1 2, but they are not vertical angles.

Checkpoint Use the Law of Detachment

If two angles from a linear pair, then they are supplementary. 3 and 4 from a linear pair. So, 3 and 4 are supplementary.

Argument 1:

If two angles from a linear pair, then they are supplementary. 3 and 4 are

supplementary. So, 3 and 4 from a linear pair.

Argument 2:

Which argument is correct? Explain your reasoning.5.

ANSWER

Argument 1 is correct. In Argument 1, the hypothesis is true, which implies that the conclusion is true. The

following counterexample shows that Argument 2 is false: Two nonadjacent angles with measures 40° and 140° are

supplementary, but they do not form a linear pair.

Example 5 Use the Law of Syllogism

Write the statement that follows from the pair of true statements.

If the daily high temperature is 32°F or less, then the water in the pipe is frozen.

If the water in the pipe is frozen, then the pipe will break.

SOLUTION

Use the Law of Syllogism.

If the daily high temperature is 32°F or less, then the pipe will break.

Checkpoint Use the Law of Syllogism

Write the statement that follows from the pair of true statements.

If the ball is thrown at the window, it will hit the window.

If the ball hits the window, then the window will break.

6.

ANSWERIf the ball is thrown at the window, then

the window will break.

Conditional StatementOriginal IF-THEN statement

Converse

When you switch both the hypothesis and conclusion

If HYPOTHESIS, then CONCLUSIONIf CONCLUSION, then HYPOTHESIS

Inverse StatementThink: INSERT

When you leave the conditional the way it is & make it negative

NOT NOT

If HYPOTHESIS, then CONCLUSION

ContrapositiveThink: COMBINATION

When you switch both the hypothesis & conclusion, AND insert a negative

BEFORE: BEFORE: If HYPOTHESIS, then CONCLUSION

NOT NOTIf CONCLUSION, then HYPOTHESIS

Things to keep in mind

If it is already Negative, and you are taking the inverse of contrapositive, then you get rid of the NOT

Conditional:Conditional:If you do NOT like cheese, then you do NOT like pizza

INVERSE: INVERSE: If you like cheese, then you like pizza

BiconditionalCombines the Condition & Converse If BOTH are true, then it is biconditionalInclude the words: IF AND ONLY IF

Example:If a shape is round, then it is a circle.If it is a circle, then the shape is a round.A shape is round, IF AND ONLY IF, it is a A shape is round, IF AND ONLY IF, it is a

circle.circle.

BiconditionalCombines the Condition & Converse If BOTH are true, then it is biconditionalInclude the words: IF AND ONLY IF

Example:If a shape is round, then it is a circle.If it is a circle, then the shape is a circle.A shape is round, IF AND ONLY IF, it is a A shape is round, IF AND ONLY IF, it is a

circle.circle.

Day 2: Logical ReasoningJanuary 29th

Unit 2

Assignment SheetAssignment SheetDatDatee


SignaturSignaturee

1-24

Textbook Assignment Page 716 & 732

___/20

1-27

Unit 2 Vocabulary

1-27

Unit 2 Book Outline ___/10

1-28

Notes on Logic Statements

1-28

AIMS Day Wkst #1

1-28

AIMS Day Wkst #2

1-28

Logic Statement HW #1 ____/5

1-29

Unit 2 Wkst #1

1-29


Updates & RemindersHomework Check!Exam corrections due TODAY!Vocab Quiz Friday


What is the difference between a converse, inverse, and contrapositive statement?

1. Draw a picture of a linear pair. Label the 2 angles. Give the angles measures.

2. Draw a picture of vertical angles & label them.

ClassworkBiconditional Wkst

ReviewFinish yesterdays

work

Day 3: Logical ReasoningJanuary 30th

Unit 2



SignaturSignaturee

1-24

Textbook Assignment Page 716 & 732

___/20

1-27

Unit 2 Vocabulary

1-27

Unit 2 Book Outline ___/10

1-28

Notes on Logic Statements

1-28

AIMS Day Wkst #1

1-28

AIMS Day Wkst #2

1-28


1-29

Unit 2 Wkst #1

1-29


1-30

Proof Introductory


Describe a biconditional statement.

(Give me 3 facts)

• Given m PQS = 12x and ∠mSQR = 5x + 5. Find x and mPQS and mSQR.

• If mPQS = 82 ◦, find its complement.

• If 1 and 2 are complementaryangles, and m1 = ( x + 2) ◦ and m2 = (5x + 4) ◦. Find the

measurement of the x.

P

Q R

S

Day 4: Logical ReasoningJanuary 31st

Unit 2



SignaturSignaturee

1-24 Textbook Assignment Page 716 & 732 ___/20

1-27 Unit 2 Vocabulary

1-27 Unit 2 Book Outline ___/10

1-28 Notes on Logic Statements

1-28 AIMS Day Wkst #1

1-28 AIMS Day Wkst #2


1-29 Unit 2 Wkst #1


1-30 Proof Introductory

1-30 Unit 2 Logic Quiz #1 ___/20

1-31 Unit 2 Vocab Quiz ___/20

1-31 Properties WKST

Proof Notes

Day 1: Logical Reasoning Unit 2. Updates & Reminders Check your grades on pinnacle Exam corrections...

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