Unit 3 Review (Logic)

Assume the statement "If P is between points Q and R, then PQ + QR = PR" is true. Which statement below represents its inverse?

• If P is not between points Q and R, then PQ + QR $\ne$ PR.

• If PQ + QR = PR, then P is between points Q and R.
  

• If PQ + QR $\ne$ PR, then P is not between points Q and R.
  

• None of the Others
  

Assuming "If  $\angle C$  and  $\angle D$  are complementary angles, then  $m\angle C\ +\ m\angle D\ =\ 90$ " is true, which phrase below would be the conclusion if you wrote the contrapositive?

•  $\angle C$  and  $\angle D$  are not complementary angles
  

•  $\angle C$  and  $\angle D$  are complementary angles
  

•  $m\angle C+m\angle D=90\degree$  

•  $m\angle C+m\angle D\ne90\degree$  

What's the best way to describe this argument?

• The conclusion is valid, satisfying the Law of Detachment.

• The conclusion is valid, satisfying the Law of Syllogism.

• The conclusion is invalid, violating the Law of Detachment.

• The conclusion is invalid, violating the Law of Syllogism.

What's the best way to describe this argument?

• The conclusion is valid, satisfying the Law of Detachment.

• The conclusion is valid, satisfying the Law of Syllogism.

• The conclusion is invalid, violating the Law of Detachment.

• The conclusion is invalid, violating the Law of Syllogism.

Suppose  $\overrightarrow{ND}$  bisects  $\angle MNY$  .Which statement below is not logically true?

•  $m\angle MND=m\angle DNY$  

•  $m\angle MNY=2\left(m\angle DNY\right)$  

•  $m\angle MNY=m\angle MND+m\angle DNY$  

•  $m\angle DNY=\frac{1}{2}\left(m\angle MND\right)$  

If  $\angle A\cong\angle B$   and  $\angle B\cong\angle C$   then  $\angle A\cong\angle C$  is a statement that satisfies what property?

• Reflexive Property
  

• Symmetric Property
  

• Transitive Property
  

• Substitution Property
  

"If  $\angle X$  and  $\angle Y$  form a linear pair, then they are supplementary angles" is an example of what property?

• Definition of Supplementary Angles
  

• Definition of a Linear Pair
  

• Supplements Theorem
  

• Congruent Supplements Theorem
  

If  $\Delta ABC$  is a right triangle, which statement below cannot be logically proven?

•  $m\angle ABD+m\angle CBD=90$  

•  $\angle BAD$  and  $\angle BCD$  are complementary.
  

•  $\angle BDA$  and  $\angle BDC$  are supplementary.
  

•  $\overline{AC}\ \perp\ \overline{BD}$  

GIVEN:  $\overline{AB}\ \perp\ \overline{BC}$  , D is the midpoint of  $\overline{AC}$ ,  $\overline{BE}$  bisects  $\angle ABD$  , and  $\overline{BF}$  is the angle bisector of  $\angle DBC$  .

Which statements below can be logically proven? (Check all that are true)

•  $m\angle ABD=45\degree$  

•  $DC=\frac{1}{2}\left(AC\right)$  

•  $m\angle EBF=45\degree$  

•  $AE+EF=CF+EF$  

•  $m\angle DBF=\frac{1}{2}\left(m\angle DBC\right)$  

What reasons justifies step 4 in the given proof?

• Segment Addition Postulate

• Addition Property of Equality

• Substitution Property

• Subtraction Property of Equality