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Proof: Conditional Statements Agenda: 1. Proof and The Axiomatic System 2. Conditional Statements 3. Proving conditional statements 4. Justification of statements 5. Debrief DO NOW 9/22: Is the statement below true? Explain/justify your answer. “If 6x + 10 = 8x, then x = 5” Proof: The Basics A proof is an argument, a justification, or a reason that something is true. It is an answer to the question “why?” when the person asking wants an argument that is indisputable. There are three basic requirements for constructing a good proof: 1. Awareness and knowledge of the definitions of the terms related to what you are trying to prove. 2. Knowledge and understanding of postulates and previous proven theorems related to what you are trying to prove. 3. Knowledge of the basic rules of logic. The Axiomatic System “Between any two points, you can draw a straight line” If B is between A and C, then AB + BC = AC Points Planes Lines “Vertical angles are congruent” Axioms/Postulates – statements accepted to be true without proof Definitions – terms generated to clarify or make more consise Undefined Terms – basic terms accepted as starting points Theorems – statements that require proof Rays Line Segments Conditional Statements “If there is a forest fire, then fish will die.” The hypothesis is the information you are assuming to be true. (“p”) The conclusion is what a proposal of what will follow from the hypothesis. (“q”) pq Using Logic in Geometry Problems Debrief Why is it important to have good notes and understandings of definitions and postulates? How can logic help you solve equations? Is logic math? Why/why not? Proof: Inductive vs. Deductive Reasoning Agenda: 1. HW Review 2. Inductive vs. Deductive 3. BBQ Logic Problem 4. Inductive Reasoning Practice 5. Debrief DO NOW 9/23: Find the next term in the sequence: Inductive vs. Deductive Reasoning Inductive Reasoning Going from observed cases to a generalized rule. Ex. I left home at 6:30 Monday, Tuesday and Wednesday, and got to school at 7:15. Therefore, if I leave home at 6:00 on Thursday, I will get to school at 7:15 Deductive Reasoning Going from a general rule to a specfic statement. Ex. The bus always takes 45 minutes to get from my hourse to school. Therefore, if I take the bus at 6:30, I will get to school at 7:15 BBQ Logic Problem Five students attended a BBQ and ate a variety of foods. Something caused some of them to become ill. Jaida ate a hamburger, pasta salad, and coleslaw. She became ill. Kyle ate coleslaw and pasta salad but not a hamburger. He became ill. De’Vonte ate only a hamburger and felt fine. Jalen didn’t eat anything and also felt fine. Tiana ate a hamburger and pasta salad but no coleslaw, and she became ill. Use inductive reasoning to make a conjecture about which food probably caused the illness. Using Inductive Reasoning to Solve Problems Debrief (EXIT TICKET) What is the difference between inductive and deductive reasoning? Proof: Vertical Angles Agenda: 1. Two Column Proofs 2. Vertical Angles 3. Statements and Justifications Jigsaw 4. Debrief Parallel Lines and a Transversal Agenda: 1. HW Review 2. Google Maps 3. Angles on Parallel Lines 4. Debrief