Day 40 Warm Up

1. Day 40 Warm Up • Use the law of syllogism to establish new information: • If I go to the beach, then I’ll surf. • If I surf, then I’ll nearly kill myself. • Aside from surfing, what will happen if I go to the beach? Monday, October 6, 2008

2. Objectives • Use the law of syllogism to reason deductively

3. Scooby Doo • Tips: • Restate all in if-then form: If the ghosts chase Scooby Doo, then he will run. • Write all with => notation. • Look for spots to apply syllogism, rearranging if necessary.

4. Scooby Doo • Therefore, if Scooby Doo asks for snacks, then he will share them with Shaggy. (After being chased by ghosts and followed by Shaggy). The rearranged statements: Scooby asks for snacks => ghosts chase Scooby ghosts chase Scooby => Scooby runs Scooby runs => Shaggy follows Shaggy follows Scooby => Scooby finds snacks Scooby finds snacks => Scooby shares

5. N*SYNC

6. Classwork • Complete the logic worksheet Home Studies • pp. 123-4 • 10, 14, 15, 24, 25 • Due Tuesday

7. Why Logic?

8. Handout

9. In Closing • Syllogism: • p => q • q => r • p => r Next Time We Meet • Pulling it all together: definitions, theorems, and logic => PROOFS

10. Day 41 Warm Up • If m and n are whole numbers, • 49 < n < 101 and 19 < m < 51, • then what is the greatest value for Image: Lori Spindler’s photostream, http://www.flickr.com/photos/lorispindler/2569943966/

11. Check Home Studies • 10. Contrapositive: “If the key is not in the ignition, then the car is not running.” • Converse: “If the key is in the ignition, then the car is running.” • 14. “If the moon is full, then the cattle will be nervous.” • 15. c., a., b., e., d. “kingdom was lost” • 24. b., e., c., a., d. “measure of <5 = 120°” • 25. c., b., e., a., d. “measure of <2 = 60°”

12. Objectives • Learn to read and create 3 styles of proofs: • Paragraph proof • Flow proof • Two-column proof • Use logical reasoning to solve puzzles.

13. Theorem 3.3 • “If two lines are perpendicular, then they intersect to form four right angles.” Source: cdw9’s photostream http://www.flickr.com/photos/wainwright/168429619/

14. Theorem 3.3 • “If two lines are perpendicular, then they intersect to form four right angles.” Prove it! p. 126 in your book Source: cdw9’s photostream http://www.flickr.com/photos/wainwright/168429619/

15. Classwork • Page 129, #9 and 10 Home Studies None Paragraph proof source: http://www.themathlab.com/geometry/mathcourt/writeproofs.htm#paragraph

16. In Closing • Paragraph proofs use full sentences for justifying steps to a conclusion. Next Time We Meet Two other forms of proof: flow & two-column. These are certainly shorter to write!

17. Jerry and Rachel are two strangers thrown together by a mysterious phone call from a woman they have never met. A doctor who is traveling to see his estranged son sparks with an unhappily married woman at a North Carolina inn. An LAPD officer will stop at nothing to force out the interracial couple who just moved in next door. A firefighter and his wife begin a 40-day experiment known as "The Love Dare" in an attempt to save their marriage. A disk containing the memoirs of a CIA agent ends up in the hands of two unscrupulous gym employees who attempt to sell it. Burn After Reading Nights in Rodanthe Fireproof Lakeview Terrace Eagle Eye Day 42 Warm Up Match the weekend’s top 5 movies with their plots. Source: http://www.imdb.com

18. Objectives • Learn to read and create 3 styles of proofs: • Paragraph proof • Flow proof • Two-column proof • Use logical reasoning to solve puzzles.

19. Paragraph Proof • Note: SAS is a theorem about triangles. We’ll learn it later. Source: http://www.homeschoolmath.net/teaching/proof.php

20. Theorems 3.4 & 3.5 • Thm 3.4: “All right angles are congruent.” • Thm 3.5: “If two lines intersect to form a pair of adjacent congruent angles, then the lines are perpendicular.” Source: Tim Caynes’ photostream http://www.flickr.com/photos/timcaynes/351502040/

21. Theorems 3.4 & 3.5 • Thm 3.4: “All right angles are congruent.” • Thm 3.5: “If two lines intersect to form a pair of adjacent congruent angles, then the lines are perpendicular.” Prove it! p. 127 in your book Source: Tim Caynes’ photostream http://www.flickr.com/photos/timcaynes/351502040/

22. Flow Proof for Thm 3.4 Thm 3.4: “All right angles are congruent.” 2 1 Given Given

23. Two-Column Proof for Thm 3.5 • Thm 3.5: “If two lines intersect to form a pair of adjacent congruent angles, then the lines are perpendicular.” 1 2 Statements Reasons 1. 1. Given

24. Ex: Problem 13 on p. 130 D C E F B

25. Classwork • p. 129 • Guided Practice 1-6 Home Studies pp. 129-131 13-19 odd

26. Classwork • Solutions for p. 129, #1-6 • Four right • perpendicular • congruent • flow • two-column • paragraph

27. In Closing • Two new theorems today – what were they? • Two new proof styles – which do you like better? Why? Next Time We Meet Proving theorems about parallel lines.

28. Day 43 Warm Up • Substitute teacher, Megan’s observing Yom Kippur. • Identify the pairs of angles that are: • Supplementary • Congruent 1 2 3 4 5 6 7 8

29. Check Home Studies

30. Objectives • Identify angles formed by two lines and a transversal. • Use properties of parallel lines, including: • Corresponding angles • Alternate interior angles • Consecutive interior angles • Alternate exterior angles • Perpendicular transversals

31. Classwork • Read and carefully study page 134 in the text. • Then solve p. 137, #1-4 Home Studies None

32. Classwork • Solutions to p. 137, #1-4 • (answers vary on all) • <1 and <5 • <3 and <5 or <4 and <6 • <1 and <7 or <2 and <8 • <4 and <5 or <3 and <6

33. Day 44 Warm Up

34. Objectives • Identify angles formed by two lines and a transversal. • Use properties of parallel lines, including: • Corresponding angles • Alternate interior angles • Consecutive interior angles • Alternate exterior angles • Perpendicular transversals

35. Parallel Lines Cut by Transversal 1 2 3 5 4 6 Red: Transversal 7 8 Yellow: Parallel lines Image: evansville’s photostream http://www.flickr.com/photos/evansville/93945229/

36. Properties of Parallel Lines • P15: Corresponding Angles Postulate • Thm 3.6: Alternate Interior Angles Thm. • Thm 3.7: Consecutive Interior Angles Thm. • Thm 3.8: Alternate Exterior Angles Thm. • Thm 3.9: Perpendicular Transversal Thm. See page 135 in the textbook.

37. Properties of Parallel Lines • P15: Corresponding Angles Postulate 1 1 & 5 are congruent 5

38. Properties of Parallel Lines • Thm 3.6: Alternate Interior Angles Thm. 2 2 & 7 are congruent 7

39. Properties of Parallel Lines • Thm 3.7: Consecutive Interior Angles Thm. 4 & 7 are supplementary 4 7

40. Properties of Parallel Lines • Thm 3.8: Alternate Exterior Angles Thm. 1 2 1 & 8 are congruent 3 5 4 6 7 8

41. Properties of Parallel Lines • Thm 3.9: Perpendicular Transversal Thm. If the red line is perpendicular to the “black dog” line then it’s also perpendicular to the “brown dog” line.

42. Classwork • p. 137, #5-8 Home Studies Starting p. 123 10, 14, 15, 24, 25 Due Monday

43. Classwork • Solutions • Perpendicular Transversal Theorem • Alternate Exterior Angles Theorem • Alternate Interior Angles Theorem • Consecutive Interior Angles Theorem • Corresponding Angles Postulate

44. In Closing • What’s a transversal? • Lots of vocabulary: corresponding angles, alternate interior angles, alternate exterior angles, consecutive interior angles. Next Time We Meet We’ll explore the problems on pages 138-9.