Reasoning & Proofs

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.

Pick the Contrapositive of the conditional statement: If an angle is 100 degrees, then the angle is obtuse.

• If an angle is not obtuse, then the angle is not 100 degrees.

• If an angle is obtuse, then the angle is 100 degrees.

• If an angle is not 100 degrees, then the angle is not obtuse.

• An angle is obtuse if and only if it is 100 degrees.

Pick the negation of the statement: I am not a math student.

• I am an english student.

• I am a math student.

• I am not a math student.

• I am not a student.

Write the conditional statement as a biconditional statement: If two lines intersect at a 90 degree angle, then those two lines are perpendicular.

• Two lines intersect at a 90 degree angle if and only if they are perpendicular.

• If two lines do not intersect at a 90 degree angle, then the two lines are not perpendicular.

• If two lines intersect at a 90 degree angle if and only if then they are perpendicular.

• If two lines are perpendicular, then they intersect at a 90 degree angle.

True or False

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

• True

• False

Which of the following is a counterexample for the statement: The absolute value of the sum of two numbers is equal to the sum of the two numbers.

• -1 and 3

• 0 and 5

• 2 and 4

• -3 and -2

What is inductive reasoning?

• When you use facts and laws of logic to form a logical argument.

• When you use patterns in a specific case and then write a conjecture for the general case.

• When you provide a specific case for which the conjecture is false.

• When you write an unproven statement based on facts.

What type of reasoning do we use when we write proofs?

• Inductive Reasoning

• Deductive Reasoning

• The Law of Syllogism

• The Law of Detachment

If a figure is a square, the it is a rectangle. You know that quadrilateral ABCD is a square. Use the Law of Detachment, what statement can you make?

• Quadrilateral ABCD is a square.

• No conclusion can be made.

• Quadrilateral ABCD is not a square.

• Quadrilateral ABCD is a rectangle.