3-1 Conjectures & Counterexamples

A concluding statement reached using inductive reasoning is called a _______

• compound statement

• conjecture

• condition

• counterexample

Tags

CCSS.7.SP.A.2

How can you prove a conjecture is false?

• Counterexample
• Not Possible
• Patterns

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

What is a counterexample?

• A generalism that cannot be applied to a specific case

• A specific case that help to prove a conjecture is true

• A general case that is supported by specific examples

• A specific case for which a conjecture is false

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

• True

• False

Tags

CCSS.L.11-12.4C

CCSS.L.6.4C

CCSS.L.7.4C

CCSS.L.8.4C

CCSS.L.9-10.4C

Complete the conjecture.
The sum of two negative numbers is ___________.

• positive
• negative
• odd
• even

Tags

CCSS.7.NS.A.1C

How many counters would come next?

• 5
• 7
• 9
• 11

Tags

CCSS.4.OA.C.5

If it is an angle, then it is acute. What is an appropriate counterexample?

• 70⁰
• 45⁰
• 120⁰
• True. There is no counterexample.

Tags

CCSS.7.G.B.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

Tags

CCSS.2.G.A.1

Which of the following provides a counterexample to the conjecture, "If two angles are supplementary, then they are not congruent."

Tags

CCSS.7.G.B.5

Which of the following provides a counterexample to the conjecture, "Vertical angles are never complementary angles."

• A right angle that's been bisected by a ray.

• 2 vertical angles with measures of 45 degrees each

• 2 angles with measurements of 30 degrees and 60 degrees

• There is no counterexample; the conjecture is true.

Tags

CCSS.7.G.B.5