Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Chapter 2: Geometric Reasoning Learning Goal: I can identify properties of equality and congruence. I can prove theorems about lines and angles using deductive reasoning and a two column proof. LESSON 2-5: ALGEBRAIC PROOFS A proof is an argument that uses logic, definitions, properties, and previously proven statements to show that a conclusion is true. An important part of writing a proof is giving justifications to show that every step is valid. Chapter 2: Geometric Reasoning Like algebra, geometry also uses numbers, variables, and operations. For example, segment lengths and angle measures are numbers. So you can use these same properties of equality to write algebraic proofs in geometry. Chapter 2: Geometric Reasoning LESSON 2-6: GEOMETRIC PROOFS When writing a proof, it is important to justify each logical step with a reason. You can use symbols and abbreviations, but they must be clear enough so that anyone who reads your proof will understand them. A theorem is any statement that you can prove. Once you have proven a theorem, you can use it as a reason in later proofs Chapter 2: Geometric Reasoning Definition of Midpoint Definition of Segment Bisector Definition of Angle Bisector Chapter 2: Geometric Reasoning Definition of Complementary Angles Definition of Supplementary Angles Definition of Linear Pairs Definition of Right Angles Definition of Straight Angles Definition of Congruent Angles Definition of Congruent Segments Vertical Angles are Congruent Chapter 2: Geometric Reasoning A geometric proof begins with Given and Prove statements, which restate the hypothesis and conclusion of the conjecture. In a twocolumn proof, you list the steps of the proof in the left column. You write the matching reason for each step in the right column. TWO COLUMN PROOFS: Given: Prove: Statement: Reason: 1. 1. 2. 2. 3. 3. 4. 4. 5. 5. 6. 6.