Thinking Geometrically: Using Proofs

Slides:



Advertisements
Similar presentations
Inverses, Contrapositives, and Indirect Reasoning
Advertisements

Inverses, Contrapositives, and Indirect Reasoning
Geometry Chapter 2 Terms.
Axiomatic systems and Incidence Geometry
Coordinate Plane Basics
Euclid BC Author of The Elements –13 books in all. –Standard textbook for Geometry for about 2000 years. Taught in Alexandria, Egypt.
The Axiomatic Method. The axiomatic method I: Mathematical Proofs Why do we need to prove things? How do we resolve paradoxes?
Spherical Geometry and World Navigation
Chapter 2 Midterm Review
Axiomatic systems By Micah McKee. VOCAB: Axiomatic system Postulate/Axiom Theorem Axiomatic system Line segment Ray Point Line Plane.
Chapter 9 Geometry © 2008 Pearson Addison-Wesley. All rights reserved.
GEOMETRY REVIEW Look how far we have come already!
MAT 333 Fall  As we discovered with the Pythagorean Theorem examples, we need a system of geometry to convince ourselves why theorems are true.
Reasoning & Proof Chapter 2.
Warm Up 8/9 1.Given the following endpoints, find the midpoint. a.(-3, -7) and (-6,2) b.(5, -9) and (-7, -25) 2.Given the following endpoint and midpoint,
Euclid’s Postulates 1.Two points determine one and only one straight line 2.A straight line extends indefinitely far in either direction 3. A circle may.
2.4 Use Postulates & Diagrams
Points, Lines, and Planes 1.2 Ms. Verdino. What will we be learning today? SPI : Use definitions, basic postulates, and theorems about points,
© 2010 Pearson Prentice Hall. All rights reserved. CHAPTER 10 Geometry.
Conditional Statements Conditional Statement: “If, then” format. Converse: “Flipping the Logic” –Still “if, then” format, but we switch the hypothesis.
INDUCTIVE REASONING AND CONJECTURE. DEFINITIONS Conjecture: a best guess based on known information. Inductive Reasoning: using specific examples to arrive.
Chapter 1 Introduction to Geometry. Slide Getting Started Points – To name a point always use Lines – All lines are and extend in both directions.
H YPERSHOT : F UN WITH H YPERBOLIC G EOMETRY Praneet Sahgal.
Euclid and the “elements”. Euclid (300 BC, 265 BC (?) ) was a Greek mathematician, often referred to as the "Father of Geometry”. Of course this is not.
Warm-Up x + 2 3x - 6 What is the value of x?. Geometry 3-3 Proving Lines Parallel.
Geometry Review 1 st Quarter Definitions Theorems Parts of Proofs Parts of Proofs.
Math 409/409G History of Mathematics Book I of Euclid’s Elements Part V: Parallel Lines.
 You will be able to use theorems and definitions to find the measures of angles.  You will be able to use theorems and definitions to write a formal.
The reason why Euclid was known as the father of geometry because, he was responsible for assembling all the world’s knowledge of flat planes and 3D geometry.
Geometry 2.2 And Now From a New Angle.
Conditional Statements A conditional statement has two parts, the hypothesis and the conclusion. Written in if-then form: If it is Saturday, then it is.
PROVING STATEMENTS IN GEOMETRY. WHAT IS A PROOF? A written account of the complete thought process that is used to reach a conclusion. Each step is supported.
Foundations of Geometry
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.
Lesson 1-5 Postulates and Theorems Relating Points, Lines, and Planes (page 22) Essential Question How are the relationships of geometric figures used.
Chapter 3: Parallel and Perpendicular Lines
Reasoning and Proof Unit 2.
Euclid’s Postulates Two points determine one and only one straight line A straight line extends indefinitely far in either direction 3. A circle may be.
Euclid’s Definitions EUCLID’ S GEOMETRY
3-3: Proving Lines Parallel
9.7 Non-Euclidean Geometries
Proofs Geometry - Chapter 2
Lesson 3-6: Perpendicular & Distance
Five-Minute Check (over Lesson 2–3) Mathematical Practices Then/Now
Proving Lines Parallel
Y. Davis Geometry Notes Chapter 2.
Euclid The Elements “There is no royal road to Geometry.”
Lesson 2.1 AIM: Conditional Statements
Geometry Review: First Semester
Chapter 2, lesson 4: Axioms and equals
2.2 Deductive Reasoning Objective:
Geometry Mathematical Reflection 2B
Five-Minute Check (over Lesson 2–4) Then/Now New Vocabulary
Chapter 2 Reasoning and Proof.
Objectives Analyze statements in if-then form.
The Elements, Book I – Propositions 22 – 28 MONT 104Q – Mathematical Journeys: Known to Unknown October 2, 2015.
3-6: Prove Theorems about Perpendicular Lines
Proofs with Parallel Lines
Parallels § 4.2 Parallel Lines and Transversals
Inequalities in Geometry
Reasoning and Proofs Deductive Reasoning Conditional Statement
Chapter 1 Tools Of Geometry
Chapter 2, lesson 5: A Simple proof
Converse Definition The statement obtained by reversing the hypothesis and conclusion of a conditional.
Logic and Reasoning.
Chapter 2: Geometric Reasoning
Advanced Geometry Section 3.7 The Isosceles Triangle Theorem/Converse/Inverse/Contrapositive Learner Objective: Students will solve proofs and problems.
Proving Lines Parallel
Chapter 2 Reasoning and Proof.
Five-Minute Check (over Lesson 2–3) Mathematical Practices Then/Now
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

Feedback: Privacy Policy Feedback
Do Not Sell My Personal Information
About project: SlidePlayer Terms of Service

© 2024 SlidePlayer.com Inc. All rights reserved.