Reasoning and Proof Unit Test Review

A statement that can be expressed in if-then form is a ...

• Converse

• Conditional

• Biconditional

• Counterexample

Answer explanation

Which choice shows a true conditional with a correctly identified hypothesis and conclusion?

• If next month is January, then this month is the last of the year.

  Hypothesis: This month is the last of the year.

  Conclusion: Next month is January.

• If next month is January, then this month is the last of the year.

  Hypothesis: Next month is January.

  Conclusion: This month is the last of the year.

Answer explanation

 

Is the following definition of complementary reversible? If yes, write it as a true biconditional.

Complementary angles are two angles whose sum measures to 90°.

• Yes, angles are complementary if their sum measures to 90°.

• Yes, angles are complementary if (and only if) their sum measures to 90°.

• Yes, if angles are complementary, then their sum measures to 90°.

• The statement is not reversible.

Answer explanation

A biconditional statement is a combination of a conditional statement and its converse written in the if and only if form.

Example: Two line segments are congruent if and only if they are of equal length.

Which biconditional is not a good definition?

• Two angles are supplementary if and only if the sum of their angles measures 180.

• Two angles are vertical angles only if they are not adjacent to each other and are formed by two intersecting lines.

• Two angles form a linear pair if and only if the angles are adjacent.

• The sum of two angles is 90 if and only if those two angles are complementary.

Answer explanation

These two angles are adjacent, however they are not a linear pair.

• Transitive Property

• Symmetric Property

• Reflexive Property

Answer explanation

The converse of a statement is formed by switching the hypothesis and the conclusion.

What is the converse of "If two angles are congruent, then they have the same measure"?

• "If two angles are not congruent, then they do not have the same measure."

• "If two angles do not have the same measure, then they are not congruent."

• “If two angles have the same measure, then they are congruent."

A counterexample is a specific case which shows that a general statement is false.

Give a counterexample for the following statement: All numbers that end in 1 are prime numbers.

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Which property is used in this problem?

• Division Property of Equality

• Subtraction Property of Equality

• Multiplication Property of Equality

• Addition Property of Equality

What is the Reason 2 in the two column proof?

• Congruent Angles

• Congruent Segments

• Given

• Symmetric Property

What is Reason 3 in the two column proof?

• Given

• Angle Addition

• Symmetric Property

• Substitution Property