unit 3 lesson 4 deductive reasoning honors geometry
TRANSCRIPT
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. AB. 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. AB. 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. AB. BC. CD. 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. AB. BC. CD. 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 othercommon sources of evidence
Let’s log our evidence!
Evidence
A. AB. BC. CD. 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
Evidence
EvidenceAngle Relationships
Evidence
Use the Perpendicular Bisector Theorems
Find the measure of PQ.
PQ = RQ Perpendicular Bisector Theorem3x + 1 = 5x – 3 Substitution
1 = 2x – 3 Subtraction property4 = 2x Addition property2 = x Division property.
So, PQ = 3(2) + 1 = 7.
Answer: 7