Inductive and deductive reasoning are both important tools in mathematics. Inductive reasoning helps you create conjectures while deductive reasoning helps you justify or prove a conjecture. As you may remember, inductive reasoning, which is used in informal proofs, is not enough on its own to prove a conjecture. Proving a conjecture means showing that it is true for all situations or examples.
Because formal geometric proofs require the use of deductive reasoning, it's important to your success in this course that you understand the difference. Use the activity below to assess your ability to identify types of reasoning. Read each scenario and decide which form of reasoning is being used in that situation.
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Alice knows that all of her teachers have taught for at least 3 years. So she knows her math teacher Ms. Davis has taught for at least 3 years.
Alice is using ________________. |
inductive reasoning
deductive reasoning
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That is correct.
You should review this topic.
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Brad has been drawing a lot of triangles in his drafting class, and he notices that the smallest angle is always opposite of the smallest side.
Brad is using_____________________. |
inductive reasoning
deductive reasoning
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That is correct.
You should review this topic.
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Charlie has been collecting flowers for his biology class, and notices that the yellow flowers always have 13 petals.
Charlie is using ________________________. |
inductive reasoning
deductive reasoning
|
That is correct.
You should review this topic.
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Derek notices that the distance formula and Pythagorean Theorem are very similar. So he uses algebra to show that the two equations are the same.
Derek is using __________________ |
inductive reasoning
deductive reasoning
|
That is correct.
You should review this topic.
Complete
