Reasoning and Proofs Part 2

A concluding statement reached using inductive reasoning is called a _______

• compound statement

• conjecture

• condition

• counterexample

Tags

CCSS.7.SP.A.2

Which of the following conjectures is false?

• The product of two even numbers is even.
• The sum of two even numbers is even.
• The product of two odd numbers is odd.
• The sum of two odd numbers is odd.

Tags

CCSS.3.OA.D.9

Refer to the following statement: "If a polygon is a quadrilateral, then it is a trapezoid."

What is a counterexample of this statement?

• If a polygon is a trapezoid, then it is a quadrilateral.

• If a polygon is not a quadrilateral, then it is not a trapezoid.

• If a polygon is not a trapezoid, then it is not a quadrilateral.

• A rectangle is also a quadrilateral.

Used to prove that a conjecture is false.

• Counterexample
• Inductive Reasoning
• Concluding statement
• Conjecture

How do you write the converse of a conditional statement?

• Negate the hypothesis and conclusion

• Reverse the hypothesis and conclusion

• Negate and reverse the hypothesis and conclusion

• Take it to Journeys and buy the converses.

Tags

CCSS.L.2.1F

CCSS.L.8.1C

CCSS.L.8.3A

Negating both the hypothesis and conclusion of the original conditional is the .....

• conditional

• converse

• inverse

• contrapositive

Original: If angles are congruent, then the measures of the angles are equal.

What is this? If angles are not congruent, then the measures of the angles are not equal.

• Conditional

• Converse

• Inverse

• Converse

Tags

CCSS.8.G.A.2

Given, "If angles are congruent, then the measures of the angles are equal." Identify the contrapositive.

• If the measures of the angles are equal, then the angles are congruent.
• If angles are not congruent, then the measures of the angles are not equal.
• If the measures of the angles are not equal, then the angles are not congruent.
• If the angles are not congruent, then the measure of the angles are equal.

Tags

CCSS.8.G.A.2

Pick the Converse of the conditional statement: If an angle is 90 degrees, then it is a right angle.

• If an angle is not 90 degrees, then it is not a right angle.

• An angle is a right angle if and only if it is 90 degrees.

• If an angle is not a right angle, then it is not 90 degrees.

• If an angle is a right angle, then it is 90 degrees.

Pick the Inverse of the conditional statement: If an angle is 30 degrees, then the angle is acute.

• If an angle is not acute, then the angle is not 30 degrees.

• If an angle is not 30 degrees, then the angle is not acute.

• If an angle is acute, then the angle is 30 degrees.

• An angle is acute if and only if it is 30 degrees.