Thinking Geometrically: Using Proofs

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Presentation transcript:

Thinking Geometrically: Using Proofs Geometry Chapter 2 Thinking Geometrically: Using Proofs

Chapter 2, Lesson 1: SWBAT Identify the hypothesis and the conclusions of a conditional Write converse (inverse and contrapositive) conditionals

Chapter 2 Lesson 1: If … then statements

Chapter 2, Lesson 1: SWBAT Identify the hypothesis and the conclusions of a conditional Write converse (inverse and contrapositive) conditionals Workbook Activities 9-10 Chapter 2: Lesson 1

Chapter 2 Lesson 2: Euclid's Five Postulates The foundation for plane geometry SWBAT: Identify postulates Construct geometric lines and shapes based on postulates

Euclid's Postulates 1. A straight line segment can be drawn joining any two points. Euclid's Postulates 2. Any straight line segment can be extended indefinitely, to form a straight line. Chapter 2: Lesson 2 Workbook Activity 11

Euclid's Five Postulates (continue) Chapter 2: Lesson 2 Workbook Activity 12

Euclid's Postulates 5: If two lines are drawn which intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough. The converse is also assumed, although not stated directly. If the inner angles are 180° or more the lines do not meet on that side. Parallel lines never meet, hence the angles on either side sum to 180°. Chapter 2: Lesson 2 Workbook Activity 11

A Euclid's Postulates Song

Chapter 2, Lesson 3 Using Euclid's Postulates (workbook Activity 13-14)

Chapter 2, Lesson 3 SWBAT: Identify postulates Construct geometric lines and shapes based on postulates

Chapter 2, Lesson 4: Axiom or Common Notions SWBAT: Identify and use axiom to solve algebraic and geometric problems

Chapter 2, Lesson 4: Axiom or Common Notions Workbook Activity 15 Workbook Activity 16

Chapter 2, Lesson 4 Theorem (Workbook Activity 17)

Chapter 2, Lesson 5, Reasoning

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