Geometry 2.2 And Now From a New Angle
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
Problem 1: Supplements and Complements
Collaborate #7 (5 Minutes)
Problem 1: Supplements and Complements
Collaborate #8 (6 Minutes)
Summary Day 1 What are complementary angles? What are supplementary angles?
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
Summary Day 1 What are complementary angles? What are supplementary angles?
Problem 2: Angle Relationships Collaborate #1 (5 Minutes) Adjacent Angles: Share a vertex and a side
Problem 2: Angle Relationships Collaborate #2 (5 Minutes) Linear Pair: Two adjacent angles that form a line
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
Problem 2: Angle Relationships We are going to do #5a together Given Statements Hypothesis: After the “If” Prove Statements Conclusion: After the “then”
D E G F
Problem 2: Angle Relationships Collaborate 4-5 (6 Minutes)
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
Problem 3 Postulates and Theorems Postulate A statement that is accepted without proof Theorem A statement that can be proven
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
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)
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
Problem 3 Postulates and Theorems Linear Pair Postulate If two angles form a linear pair, then the angles are supplementary Collaborate #1 (2 Minutes)
Problem 3 Postulates and Theorems
Summary Addition Property of Equality
Summary Subtraction Property of Equality
Summary Reflexive Property
Summary Substitution Property
Summary Transitive Property
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
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
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