Counterexamples

Front

What is a counterexample?

Back

A counterexample is an example that disproves a statement or claim. It shows that the statement is not always true.

Front

If two angles are supplementary, what does it mean?

Back

Two angles are supplementary if their measures add up to 180 degrees.

Tags

CCSS.7.G.B.5

Front

Provide a counterexample to the statement: 'If two angles are supplementary, then they are not congruent.'

Back

90° and 90° are supplementary angles that are congruent.

Tags

CCSS.7.G.B.5

Front

What is the definition of a supplementary angle?

Back

Supplementary angles are two angles whose sum is 180 degrees.

Tags

CCSS.7.G.B.5

Front

What is the purpose of a counterexample in mathematics?

Back

The purpose of a counterexample is to demonstrate that a general statement is false by providing a specific instance where the statement does not hold.

Tags

CCSS.HSF-BF.B.4D

Front

Provide a counterexample to the statement: 'If an animal is brown, then it is a dog.'

Back

A squirrel is a brown animal that is not a dog.

Front

What is a necessary condition in a conditional statement?

Back

A necessary condition is a condition that must be true for the statement to be true.

Front

What is a sufficient condition in a conditional statement?

Back

A sufficient condition is a condition that, if true, guarantees the truth of the statement.

Front

Provide a counterexample to the statement: 'If you add two numbers, then the sum is odd.'

Back

2 + 4 = 6, which is an even sum.

Tags

CCSS.3.OA.D.9

Front

What is the difference between a necessary and sufficient condition?

Back

A necessary condition must be true for the statement to hold, while a sufficient condition guarantees the statement's truth.