1. Geometry 2.2 And Now From a New Angle

2. 2.2 Special Angles and Postulates: Day 1  Objectives  Calculate the complement and supplement of an angle  Classify adjacent angles, linear pairs, and vertical angles  Differentiate between postulates and theorems  Differentiate between Euclidean and non- Euclidean geometries

4. Problem 1: Supplements and Complements

6.  Collaborate #7 (5 Minutes)

7. Problem 1: Supplements and Complements

10.  Collaborate #8 (6 Minutes)

13. Summary Day 1  What are complementary angles?  What are supplementary angles?

14. 2.2 Special Angles and Postulates: Day 2  Objectives  Calculate the complement and supplement of an angle  Classify adjacent angles, linear pairs, and vertical angles  Differentiate between postulates and theorems  Differentiate between Euclidean and non- Euclidean geometries

15. Summary Day 1  What are complementary angles?  What are supplementary angles?

16. Problem 2: Angle Relationships  Collaborate #1 (5 Minutes)  Adjacent Angles: Share a vertex and a side

17. Problem 2: Angle Relationships  Collaborate #2 (5 Minutes)  Linear Pair: Two adjacent angles that form a line

18. Problem 2: Angle Relationships  Collaborate #3 (5 Minutes)  Vertical Angles: Nonadjacent angles formed by intersecting lines  Vertical Angles are congruent Need Protractors for part d

19. Problem 2: Angle Relationships  We are going to do #5a together  Given Statements  Hypothesis: After the “If”  Prove Statements  Conclusion: After the “then”

20. D E G F

21. Problem 2: Angle Relationships  Collaborate 4-5 (6 Minutes)

25. Formative Assessment Day 2  Performance Task Unit 2  Use protractor for #1 and #2  Take home to finish  Must be turned in by tomorrow  You may turn in today if you finish  We will complete the student rubric on Monday  Formative 16 points

26. Problem 3 Postulates and Theorems  Postulate  A statement that is accepted without proof  Theorem  A statement that can be proven

27. Euclidean Geometry 1. A straight line segment can be drawn joining any two points 2. Any straight line segment can be extended indefinitely in a straight line 3. Given any straight line segment, a circle can be drawn that has the segment as its radius and one endpoint as center 4. All right angles are congruent

28. Euclidean Geometry 5. If two lines are drawn that intersect a third line in such a way that the sum of the inner angles of one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough. (Parallel Postulate)

29. Euclid’s Elements  The five “common notions” 1. Things that equal the same thing also equal one another 2. If equals are added to equals, then the wholes are equal 3. If equals are subtracted from equals, then the remainders are equal 4. Things that coincide with one another equal one another 5. The whole is greater than the part

30. Problem 3 Postulates and Theorems  Linear Pair Postulate  If two angles form a linear pair, then the angles are supplementary  Collaborate #1 (2 Minutes)

31. Problem 3 Postulates and Theorems

33. Summary Addition Property of Equality

34. Summary Subtraction Property of Equality

35. Summary Reflexive Property

36. Summary Substitution Property

37. Summary Transitive Property

38. Summary Parallel Lines and Angles  If 2 lines are parallel, …………………  Corresponding Angle Postulate  Then Corresponding Angles Congruent  Alternate Interior Angle Theorem  Then Alternate Interior Angles Congruent  Alternate Exterior Angle Theorem  Then Alternate Exterior Angles Congruent  Same-Side Interior Angle Theorem  Then Same-Side Interior Angles are Supplementary  Same-Side Exterior Angle Theorem  Then Same-Side Exterior Angles are Supplementary

39. Formative Assessment Day 3  Skills Practice 2.2  Vocabulary – All  Problem Set  Need a protractor (1-16) - SKIP  Do all of the ODD problems (17-25)  Do all (27-50)  End of Chapter Test for Review  Quiz Tomorrow  We will discuss the review before you leave today

40. 2.2 Special Angles and Postulates: Day 4  Get out Skills Practice 2.2  Vocabulary  (17-50) Odd  Formative Assessment Quiz 2.2 (10 Points)  You may write on the test  Please scan when you turn in  Assignments 2.2  Please pick-up when you are finished with the quiz  You will need a protractor also