1. Day 1: Logical Reasoning Unit 2

2. Updates & Reminders Check your grades on pinnacle Exam corrections due tomorrow Vocab Quiz Friday

3. Warm Up & Journal Describe in your own words how to construct a congruent angle.

4. Assignment Sheet DateAssignmentGradeSignature 1-24Textbook Assignment Page 716 & 732____/20 1-27Unit 2 Vocabulary 1-27Unit 2 Book Outline____/10 1-28Notes on Logic Statements 1-28Gap Day Wkst #1 1-28Gap Day Wkst #2 1-28Logic Statement HW #1____/5

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.

6. 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.

7. 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. ANSWER You can conclude that the cotton T-shirt shrinks.

8. 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.

9. 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.

10. 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.

11. 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.

12. 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.

13. 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. ANSWER If the ball is thrown at the window, then the window will break.

14. Conditional Statement Original IF-THEN statement

15. Converse When you switch both the hypothesis and conclusion If HYPOTHESIS, then CONCLUSION If CONCLUSION, then HYPOTHESIS

16. Inverse Statement Think: INSERT When you leave the conditional the way it is & make it negative NOT NOT If HYPOTHESIS, then CONCLUSION

17. Contrapositive Think: COMBINATION When you switch both the hypothesis & conclusion, AND insert a negative BEFORE: BEFORE: If HYPOTHESIS, then CONCLUSION NOT NOT If CONCLUSION, then HYPOTHESIS

18. Things to keep in mind If it is already Negative, and you are taking the inverse of contrapositive, then you get rid of the NOTConditional: If you do NOT like cheese, then you do NOT like pizzaINVERSE: If you like cheese, then you like pizza

19. Biconditional Combines the Condition & Converse If BOTH are true, then it is biconditional Include 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 circle. A shape is round, IF AND ONLY IF, it is a circle.

20. Biconditional Combines the Condition & Converse If BOTH are true, then it is biconditional Include 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 circle. A shape is round, IF AND ONLY IF, it is a circle.

21. Day 2: Logical Reasoning January 29 th Unit 2

22. Assignment Sheet DateAssignmentGradeSignature 1-24Textbook Assignment Page 716 & 732___/20 1-27Unit 2 Vocabulary 1-27Unit 2 Book Outline___/10 1-28Notes on Logic Statements 1-28AIMS Day Wkst #1 1-28AIMS Day Wkst #2 1-28Logic Statement HW #1____/5 1-29Unit 2 Wkst #1 1-29Logic Statement HW #2____/5

23. Updates & Reminders Homework Check! Exam corrections due TODAY! Vocab Quiz Friday

24. Warm Up & Journal 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.

25. Classwork Biconditional Wkst Review Finish yesterdays work

26. Day 3: Logical Reasoning January 30 th Unit 2

27. Assignment Sheet DateAssignmentGradeSignature 1-24Textbook Assignment Page 716 & 732___/20 1-27Unit 2 Vocabulary 1-27Unit 2 Book Outline___/10 1-28Notes on Logic Statements 1-28AIMS Day Wkst #1 1-28AIMS Day Wkst #2 1-28Logic Statement HW #1____/5 1-29Unit 2 Wkst #1 1-29Logic Statement HW #2____/5 1-30Proof Introductory

28. Warm Up & Journal Describe a biconditional statement. (Give me 3 facts) Given m ∠ PQS = 12x and m  SQR = 5x + 5. Find x and m  PQS and m  SQR. If m  PQS = 82 ◦, find its complement. If  1 and  2 are complementary angles, and m  1 = ( x + 2) ◦ and m  2 = (5x + 4) ◦. Find the measurement of the x. P QR S

29. Day 4: Logical Reasoning January 31 st Unit 2

30. Assignment Sheet DateAssignmentGradeSignature 1-24Textbook Assignment Page 716 & 732___/20 1-27Unit 2 Vocabulary 1-27Unit 2 Book Outline___/10 1-28Notes on Logic Statements 1-28AIMS Day Wkst #1 1-28AIMS Day Wkst #2 1-28Logic Statement HW #1____/5 1-29Unit 2 Wkst #1 1-29Logic Statement HW #2____/5 1-30Proof Introductory 1-30Unit 2 Logic Quiz #1___/20 1-31Unit 2 Vocab Quiz___/20 1-31Properties WKST

31. Proof Notes