Deductive Reasoning 1

Reasoning based on facts, definitions, accepted properties, and the laws of logic is called ____________ reasoning.

• Inductive

• Deductive

Which of the following is a valid conditional statement for the following phrase:

An acute angle has a measure less than 90°.

• If an angle is acute, then it has a measure less than 90°.

• If an angle is not acute, then it does not have a measure less than 90°.

• If an angle is acute, then it is acute.

• If an angle does not measure less than 90°, then it is not acute.

Consider the following statements.
p: The sum of two angles is 180 degrees
q: The two angles are supplements
Which of the following is a symbolic representation of:
If two angles are not supplements, then the sum of the two angles is not 180 degrees.

Tags

CCSS.4.MD.C.7

Conditional: If Jenny buys a guitar, then she will not buy a keyboard.
What is this? If Jenny does buy a keyboard, then she will not buy a guitar.

• Converse
• Inverse
• Contrapositive
• Negation

Reasoning based on specific examples and patterns used to form conjectures is called ______________ reasoning.

• Inductive

• Deductive

Transform the statement “Points that lie on the same line are collinear” into if-then form.

• If they lie on the same line, they are collinear.

• If they are collinear, they are points on the same line.

• If they are collinear, then they are points.

• If points lie on the same line, then they are collinear.

If the conditional statement was "If an angle is acute, then it has a measure less than 90°.", which type of statement is the following?

An angle is acute if and only if (iff) it has a measure less than 90°.

• Biconditional

• Converse

• Inverse

• Contrapositive

Identify the hypothesis and conclusion of the conditional statement:
If you give me twenty dollars, then I will be your best friend.

• Hypothesis: I will be your best friend
  Conclusion: you give me twenty dollars
• Hypothesis: you give me twenty dollars
  Conclusion: I will be your best friend
• Hypothesis: if you have to pay for friends
  Conclusion: then you probably should reevaluate your life
• Hypothesis: you will not have to pay twenty dollars
  Conclusion: if you have lots of friends

If the conditional statement was "If an angle is acute, then it has a measure less than 90°.", which type of statement is the following?

If an angle does not have a measure less than 90°, then it is not acute.

• Contrapositive

• Converse

• Biconditional

• Inverse

Given, "If I have a Siberian Husky, then I have a dog." Identify the contrapositive.

• If I do not have a Siberian Husky, then I do not have a dog.
• If I have a dog, then I have a Siberian Husky.
• If I do not have a dog, then I do not have a Siberian Husky.
• If I do not have a Siberian Husky, then I have a dog. 

Tags

CCSS.RI.7.8

CCSS.RI.8.1

CCSS.RI.8.8

CCSS.RL.8.1

CCSS.RL.9-10.1