Unit 3 Lesson 4 Deductive Reasoning Honors Geometry

Objectives I can use deductive reasoning to determine if conclusions are valid I can provide evidence for conclusions

Deductive Reasoning The use of facts, rules, definitions, properties, etc to reach logical conclusions DO NOT base conclusions on: – A pattern of previous behavior / occurrences – Personal observation (that looks parallel) – Assumption These are examples of Inductive Reasoning

Inductive and Deductive Reasoning WEATHER Determine whether the conclusion is based on inductive or deductive reasoning. In Miguel’s town, the month of April has had the most rain for the past 5 years. He thinks that April will have the most rain this year. Answer: Miguel’s conclusion is based on a pattern of observation, so he is using inductive reasoning. The conclusion is NOT valid.

A.A B.B Determine whether the conclusion is based on inductive or deductive reasoning. Macy’s mother orders pizza for dinner every Thursday. Today is Thursday. Macy concludes that she will have pizza for dinner tonight. A.Inductive (invalid) B.Deductive (valid)

A.A B.B Determine whether the conclusion is based on inductive or deductive reasoning. The library charges $0.25 per day for overdue books. Kyle returns a book that is 3 days overdue. Kyle concludes that he will be charged a $0.75 fine. A.Inductive (invalid) B.Deductive (valid)

Evidence In order to use deductive reasoning in Geometry, you must offer evidence for your conclusions – Definitions – Theorems – Postulates We will review some possible evidences that are frequently used

Evidence The properties of equality Performing operations to both sides of an equation? Offer these as reasons / evidence

Evidence The properties of equality If you need to manipulate an equation? Use one of these:

Note Properties of equality carry over to congruence BUT do not offer a property of equality as evidence for congruence – Ex: use the transitive property of congruence

A.A B.B C.C D.D A.Transitive Property B.Symmetric Property C.Reflexive Property D.Segment Addition Postulate Justify the statement with a property of equality or a property of congruence.

A.A B.B C.C D.D A.Distributive Property B.Addition Property C.Substitution Property D.Multiplication Property State the property that justifies the statement. 2(LM + NO) = 2LM + 2NO

Evidence Now we will make note of several other common sources of evidence Let’s log our evidence!

Evidence

A.A B.B C.C D.D A.WX > WZ B.XW + WZ = XZ C.XW + XZ = WZ D.WZ – XZ = XW State a conclusion that can be drawn from the statements given using the property indicated. W is between X and Z; Segment Addition Postulate.

Evidence

Evidence Angle Relationships

Evidence

Use the Perpendicular Bisector Theorems Find the measure of PQ. PQ= RQPerpendicular Bisector Theorem 3x + 1= 5x – 3Substitution 1= 2x – 3Subtraction property 4= 2xAddition property 2= xDivision property. So, PQ = 3(2) + 1 = 7. Answer: 7