Suppose you just got your driver’s license. You are begging your parents to buy you a car, but they refuse. An argument you might make is that ALL the kids at school are getting a new car when they get their license.
Does that argument work?
Is the statement, “All my friends are getting a car when they get their license” even true?
Interactive popup. Assistance may be required. Not unless every single student at your school gets a car when they get their license.Your parents could easily disprove this statement. How?
It only takes one counterexample to show that your statement is false.
What's a counter example that your parents could use to disprove the claim about your friends getting a car?
In geometry, for a statement to have a truth value of TRUE, it must always be true. Sometimes, it just takes some clarification to make the statement true. For example, if we said, "For three collinear points P, Q, and R, then PQ + QR = PR.
Is this always true, sometimes true, or never true?
TRUE here:
NOT TRUE here:
How can you change the statement to make it always true?
A statement or conjecture can be written based on seeing several examples. This is called using inductive reasoning. Sometimes a conjecture made this way seems true, but one counter example proves it to be false.
Example:
Conjecture: The exterior angles of a regular polygon are acute.