3-1 Conjectures & Counterexamples

A concluding statement reached using inductive reasoning is called a _______

• compound statement

• conjecture

• condition

• counterexample

How can you prove a conjecture is false?

• Counterexample
• Not Possible
• Patterns

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

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

• positive
• negative
• odd
• even

How many counters would come next?

• 5
• 7
• 9
• 11

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

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

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

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.