Reasoning and Proof Unit 2.

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Presentation transcript:

Reasoning and Proof Unit 2

Unit 2 - Reasoning and proof Learning Objectives: Learn about reasoning Make logical argument and conclusion Justify steps of by postulate or theorem Provide a convincing argument Refine the thinking process

Unit 2 - Reasoning and proof 2-1 Inductive and Deductive reasoning 2-2 Conditional statements 2-3 Postulate and Diagrams 2-4 Algebraic Reasoning 2-5 Proving Geometric Relationships

2-1 Inductive and Deductive Reasoning Key Terms Inductive reasoning: making specific observations and then drawing broad conclusions or conjecture based on those observations. Deductive reasoning: the reasoning from proven facts, postulates, theorems, definition using logically valid steps to arrive at a conclusion. Postulate: A postulate is a statement that is assumed to be true without a proof. Example: Through any two points in a plane there is exactly one straight line. Theorem: A theorem is a statement that can be proven to be true based upon postulates and previously proven theorems. Example: The measures of the angles of a triangle add to 180 degrees. 2-1 Inductive and Deductive Reasoning

2-1 Inductive and Deductive Reasoning Define inductive reasoning. Define deductive reasoning. Apply inductive reasoning. Use deductive reasoning. Understand the difference between inductive and deductive reasoning. Lesson Aim:

Examples of Inductive Reasoning Question: What is the next term of this sequence? 1,3,5,7,9,11,… Answer: When you look at the pattern in the sequence of numbers, you notice number increased by 2. Therefore by inductive reasoning you can conclude that the next number is 13. Question: What is the next shape ? Examples of Inductive Reasoning

Examples of Inductive Reasoning Q: What is the next shape? A: Looking at the first three shapes with 3, 4, 5 sides leads you to believe that the next shape should have 6 sides. This is a type of logical reasoning called inductive reasoning which is based on studying patterns. Q: What is the next number in the sequence? 1/2, 2/6, 3/18, …. A: Looking at the first numbers leads you to conclude that the next number is 4/54. This is an inductive reasoning because of the pattern. Examples of Inductive Reasoning

2-1 Inductive and Deductive Reasoning

2-1 Inductive and Deductive Reasoning