Conjectures and counterexamples

Front

What is a conjecture?

Back

A conjecture is a statement or proposition that is believed to be true based on observations but has not yet been proven.

Front

What is a counterexample?

Back

A specific case for which a conjecture is false.

Front

What does inductive reasoning involve?

Back

Testing and observing patterns to make conjectures.

Front

If two angles are supplementary, what can we say about their measures?

Back

The sum of their measures is 180°.

Front

Provide an example of a counterexample to the conjecture: 'All angles are acute.'

Back

120° is a counterexample because it is not acute.

Front

What is deductive reasoning?

Back

Deductive reasoning involves drawing specific conclusions from general principles or premises.

Front

What is the difference between inductive and deductive reasoning?

Back

Inductive reasoning makes generalizations based on specific observations, while deductive reasoning applies general principles to reach specific conclusions.

Front

What is the sum of two supplementary angles?

Back

180°.

Front

What is an acute angle?

Back

An angle that measures less than 90°.

Front

What is a right angle?

Back

An angle that measures exactly 90°.