Question

1. give your own example of inductive reasoning and inductive reasoning. explain how you know your example demonstrates inductive or deductive reasoning.

inductive:
deductive:

1. kaitlyn recently learned in her geometry class that vertical angles are congruent. she uses her protractor and measures different vertical angles in her notebook, and notices that they are in fact congruent. she thinks that this is an example of inductive reasoning.

is she correct? explain how you know.

Explanation:

Inductive reasoning involves generalizing from specific examples. Deductive reasoning starts with a general principle and applies it to specific cases.

For the inductive example: Suppose I observe that every time I drop a pen, it falls. I generalize that all pens (and similar objects) will fall when dropped. This is inductive as it's based on specific observations leading to a general conclusion.

For the deductive example: All mammals have hair. A dog is a mammal. So, a dog has hair. Here, we start with a general rule (mammals have hair) and apply it to a specific case (a dog).

Regarding Kaitlyn: She is incorrect. Since she is using a general principle (vertical angles are congruent - a proven geometric theorem) and then verifying it with specific examples (measuring in her notebook), this is deductive reasoning. The general principle (the theorem) is used to check specific instances.

Answer:

Inductive example: Observing pens falling and generalizing all pens will fall. Based on specific to general.
Deductive example: All mammals have hair; dog is mammal; so dog has hair. Based on general to specific.
Kaitlyn: No. She uses a general geometric theorem (vertical angles congruent) to check specific cases (her measurements) → deductive.