9.2 Inductive and Deductive Reasoning

Identify the hypothesis of this conditional:
If Sally goes to the park, then she will fall off the swing.

• Sally goes to the park.
• Sally will fall off the swing.
• Parks don't have swings that Sally goes to.
• If Sally falls off the swing, she goes to the park.

Tags

CCSS.L.2.1F

CCSS.L.8.1C

CCSS.L.8.3A

Identify the conclusion to the following:
If Spencer wins his soccer game, then he will be happy.

• Spencer is happy
• Spencer is not happy
• Spencer lost his game.
• Spencer is not happy if he does not win his soccer game.

Tags

CCSS.L.2.1F

CCSS.L.8.1C

CCSS.L.8.3A

Write the statement below as a conditional statement.

Vertical Angles are congruent

• Two angles are vertical if and only if they are congruent.

• If two angles are congruent, then they are Vertical.

• If two angles are Vertical, then they are congruent.

When writing a biconditional statement, we use the phrase ___ between the hypothesis and conclusion.

• if

• then

• if and only if

• always

What is the biconditional that matches the statement: "A right angle is an angle with 90 degrees."

• If an angle has 90 degrees, then it is a right angle.
• If an angle is a right angle, then it has 90 degrees.
• An angle is a right angle if and only if it has 90 degrees.

Tags

CCSS.7.G.B.5

• This statement cannot be written as a true biconditional. 

Test the statement below to see if it is reversible. If so, write it as a biconditional.

Complementary angles are two angles with measures that have a sum of 90.

• Reversible; If two angles are complementary, then the sum of their measures is 90.

• Reversible; Two angles are complementary if and only if the sum of their measures is 90.

• Not reversible.

Tags

CCSS.7.G.B.5

Which of the following statements are true biconditionals?

• x = 10 if and only if 3x + 2 = 28.

• 3x + 2 = 11 if and only if x = 3.

Consider the statement:

If Julie eats tomatoes, then she likes salad.

Is the statement TRUE/FALSE/Cannot be determined?

• True

• False

• Cannot be determined

Tags

CCSS.L.2.1F

CCSS.L.8.1C

CCSS.L.8.3A

When can a biconditional statement be true?

• When the inverse and the converse are both true
• When the original statement (conditional statement) & the contrapositive are both true.
• When the converse is true.
• When the original statement (conditional statement) and the converse are both true.