ACP Review #1: Logic

• If two angles are not acute, then they are not congruent.

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

• If two angles are not congruent, then they are acute.

• If two angles are not congruent, then they are not acute.

Answer explanation

An INVERSE negates the hypothesis (p) and conclusion (q) without switching the order of the sentence.

• a

• b

• c

• d

Answer explanation

Supplementary just means TWO angles add up to 180. A linear pair is two angles that add up to 180 AND must be connected (adjacent) to each other.

• a

• b

• c

• d

Answer explanation

The INVERSE negates the hypothesis (p) and the conclusion (q) of the statement.

• a

• b

• c

• d

Answer explanation

A FALSE biconditional is when the original statement is true, but its converse is false. It is True that Vertical Angles are Congruent. It is NOT necessarily true that if angles are congruent that they have to be vertical angles in their arrangement.

• a

• b

• c

• d

Answer explanation

A COUNTEREXAMPLE is an example that proves a statement FALSE. In this case, we need 3 points that ARE coplanar, but NOT collinear.

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Answer explanation

The VERTEX is the pointy part or corner of the angles (where their rays come to join). Just because the vertices of two angles are touching doesn't mean they have to also share a side (be adjacent)....

Which statement represents the logical equivalent of the conditional? (G.4B)

• If x=9, then 2x-5.

• If 2x-5≠13, then x≠9.

• If x≠9, then 2x-5≠13.

• x = 9 if and only if 2x-5=13.

Answer explanation

Remember that "logically equivalent" or "same truth value" or "same meaning" are all key phrases where we need to pick the CONTRAPOSITIVE statement: Switch and 2 Not's