Counterexamples

Which of the following provide a counterexample to the claim:

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

•  $40\degree\ and\ \ 140\degree$ 

•  $80\degree\ and\ \ 80\degree$ 

•  $30\degree\ and\ \ 150\degree$ 

•  $90\degree\ and\ \ 90\degree$ 

Tags

CCSS.HSG.CO.C.9

Which is a counterexample to the following statement?

If an angle is obtuse, then it is $125\degree$ .

•  $90\degree$  

•  $57\degree$  

•  $160\degree$  

•  $180\degree$  

Tags

CCSS.HSG.CO.A.1

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

What is a counterexample?

• A generalism that cannot be applied to a specific case

• A specific case that help to prove a conjecture

• A general case that is supported by specific examples

• A specific case for which a conjecture is false

Provide a counterexample to the following claim:

"All quadrilaterals have at least one set of parallel sides."

• Trapezoid

• Rectangle

• Rhombus

• Kite

Provide a counterexample to the following claim:

"If a shape has four congruent sides, then it is a square."

Tags

CCSS.5.G.B.3

CCSS.5.G.B.4

Which of the following is a counterexample:

No square has an area equal to its perimeter.

• 3 by 3 square

• 2 by 2 square

• 1 by 1 square

• 4 by 4 square

Tags

CCSS.4.MD.A.3

If it is a fraction, then it is a number between zero and one. What is an appropriate counterexample?

• 2/3
• 4/5
• 1/2
• 3/2

Tags

CCSS.4.NF.A.2

CCSS.4.NF.B.3

Which of the following is a counterexample to the following conjecture? If  $x^2\ =\ 4$ , then x = 2

• x = 4

• x = -2

• x = 2

• x = -4

Tags

CCSS.HSA.REI.A.2

CCSS.HSA.REI.B.4