Counterexamples

A counterexample is an example that proves a conjecture to be true.

• True

• False

To fully disprove a conjecture, one needs to find only ONE counterexample.

• True

• False

• x = 4

• x = -2

• x = 2

• x = -4

Tags

CCSS.HSA.REI.A.2

CCSS.HSA.REI.B.4

How many counters would come next?

• 5
• 7
• 9
• 11

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.IF.A.3

CCSS.HSF.LE.A.2

How can you prove a conjecture is false?

• Counterexample
• Not Possible
• Patterns

If an animal is furry, then it is a hamster. What would be an appropriate counterexample?

• goldfish
• frog
• elephant
• cat

Tags

CCSS.HSS.CP.A.5

Which is a counterexample of: If a four sided shape has two sides the same length, then it must be a rectangle.

• quadrilateral
• rectangle
• square
• triangle

Which of the following provide a counterexample to the claim:

"If two angles are supplementary, then they are not congruent."

Tags

CCSS.HSG.CO.C.9

Tags

CCSS.HSG.CO.A.1

If two lines have the same slope, they must be parallel. Identify a counterexample.

• They lines are perpendicular.

• The lines coincide (lie on top of one another/same line).

• They are opposite reciprocal.

• There is no counterexample.

Tags

CCSS.HSG.CO.C.9

CCSS.HSG.GPE.B.5