Honors Geometry Intro. to Deductive Reasoning

1. Honors GeometryIntro. to Deductive Reasoning

2. Reasoning based on observing patterns, as we did in the first section of Unit I, is called inductivereasoning. A serious drawback with this type of reasoning is your conclusion is not always true.

3. The logic chains we worked with in Section 2.2 are examples of deductive reasoning.*Deductive reasoning is reasoning based onDeductive reasoning logically correct conclusions always give a correct conclusion.

4. We will reason deductively by doing two column proofs. In the left hand column, we will have statements which lead from the given information to the conclusion which we are proving. In the right hand column, we give a reason why each statement is true. Since we list the given information first, our first reason will always be ______. Any other reason must be a _________, _________ or ________. given theorem postulate definition

5. A theoremis a statement which can be proven. We will prove our first theorems shortly.

6. Our first proofs will be algebraic proofs. Thus, we need to review some algebraic properties. These properties, like postulates are accepted as true without proof.

7. Reflexive Property of Equality: Symmetric Property of Equality: a= a If a = b, then b = a

8. Addition Property of Equality:Subtraction Property of Equality:Multiplication Property of Equality: If a = b, then a+c=b+c If a = b, then a-c = b-c If a = b, then ac =bc

9. Division Property of Equality:

10. Substitution Property: If two quantities are equal, then one may be substituted for the other in any equation or inequality.

11. Distributive Property (of Multiplication over Addition): a(b+c) = ab + ac

12. Example: Complete this proof: Given Multiplication Property Distributive Property Addition Property Division Property

13. Example: Prove the statement: 1. Given