Counterexamples

Front

What is a counterexample?

Back

A counterexample is an example that disproves a conjecture or statement.

Front

True or False: A counterexample proves a conjecture to be true.

Back

False

Front

What does it mean if two angles share a common vertex but are not adjacent?

Back

It means that the statement 'If two angles share a common vertex, then they are adjacent' is false, and a counterexample exists.

Front

What is a conditional statement?

Back

A conditional statement is an if-then statement that asserts a relationship between two propositions.

Front

Provide an example of a conditional statement.

Back

If it rains, then the ground will be wet.

Front

What is the purpose of a counterexample in mathematics?

Back

The purpose of a counterexample is to demonstrate that a conjecture or statement is not universally true.

Front

If an angle is obtuse, what is the minimum degree measure it can have?

Back

An obtuse angle must be greater than 90 degrees.

Front

What is a valid counterexample to the statement: 'If an angle is obtuse, then it is 125 degrees'?

Back

160 degrees is a valid counterexample.

Front

What does it mean for points to be coplanar?

Back

Coplanar points are points that lie on the same plane.

Front

What is a counterexample to the statement: 'If 3 points are coplanar, then they are collinear'?

Back

A set of three points that form a triangle is a counterexample.