2.1 Use Inductive Reasoning
Geometry, like much of science and mathematics, was developed partly as a result of people recognizing and describing patterns. In this lesson, you will discover patterns yourself and use them to make predictions.
Goal: How do you use inductive reasoning in mathematics?
Vocabulary
INDUCTIVE REASONING
Conjecture- is an unproven statement that is based on observations.
Inductive Reasoning-you use when you find a pattern in specific cases and then write a conjecture for the general case.
DISPROVING CONJECTURES
To show that a conjecture is true, you must show that is is true of all cases. You can show that a conjecture is false, however, by simply finding counterexamples.
Counterexample- is a specific case for which the conjecture is false.
Geometry, like much of science and mathematics, was developed partly as a result of people recognizing and describing patterns. In this lesson, you will discover patterns yourself and use them to make predictions.
Goal: How do you use inductive reasoning in mathematics?
Vocabulary
INDUCTIVE REASONING
Conjecture- is an unproven statement that is based on observations.
Inductive Reasoning-you use when you find a pattern in specific cases and then write a conjecture for the general case.
DISPROVING CONJECTURES
To show that a conjecture is true, you must show that is is true of all cases. You can show that a conjecture is false, however, by simply finding counterexamples.
Counterexample- is a specific case for which the conjecture is false.
Example 1: Patterns and inductive reasoning
Example 2: Make an conjecture
Example 3:
Example 4:
