Module 2 Logic & Reasoning Test

A two-column proof is an example of (a)   .

• Theorem

• Proof

• Example

• Statement

A (a)   is a pair of adjacent angles whose noncommon sides are opposite rays.

• conditional statement

• contrapositive

• deductive reasoning

• linear pair

The statement "If a number is divisible by 2, then it is even" is an example of a (a)   ?

• Definition

• Theorem

• Conjecture

• Axiom

A statement formed by both exchanging and negating the hypothesis and conclusion of a conditional statement is the (a)   .

• Contrapositive

• Inverse

• Converse

• Conditional

Write the definition of the term as a biconditional statement. obtuse angle.

• An angle is obtuse if and only if it measures more than 90 degrees and less than 180 degrees.

• An angle is obtuse if and only if it measures exactly 90 degrees.

• An angle is obtuse if and only if it measures less than 90 degrees.

• An angle is obtuse if and only if it measures exactly 180 degrees.

Write the definition of the term as a biconditional statement. pentagon.

• A figure is a pentagon if and only if it has five sides.

• A figure is a pentagon if and only if it has four sides.

• A figure is a pentagon if and only if it has six sides.

• A figure is a pentagon if and only if it has three sides.

Write the statement "Monday is a weekday" in if-then form. Then write the converse, inverse, and contrapositive of the statement.

• If it is Monday, then it is a weekday. Converse: If it is a weekday, then it is Monday. Inverse: If it is not Monday, then it is not a weekday. Contrapositive: If it is not a weekday, then it is not Monday.

• If it is Monday, then it is a weekday. Converse: If it is a weekday, then it is Monday. Inverse: If it is not a weekday, then it is not Monday. Contrapositive: If it is not Monday, then it is not a weekday.

• If it is Monday, then it is a weekday. Converse: If it is not a weekday, then it is not Monday. Inverse: If it is not Monday, then it is not a weekday. Contrapositive: If it is a weekday, then it is Monday.

• If it is Monday, then it is a weekday. Converse: If it is a weekday, then it is Monday. Inverse: If it is not Monday, then it is not a weekday. Contrapositive: If it is not a weekday, then it is not Monday.

A triangle with three acute angles is an acute triangle. Triangle RST has three acute angles. Use deductive reasoning to write a conclusion.

• Triangle RST is an obtuse triangle.

• Triangle RST is a right triangle.

• Triangle RST is an acute triangle.

• Triangle RST is an equilateral triangle.

Decide if inductive reasoning or deductive reasoning is used to reach the conclusion. All acute angles measure less than 90°. ∠LMN is an acute angle, so ∠LMN has a measure less than 90°.

• Inductive reasoning

• Deductive reasoning

Decide if inductive reasoning or deductive reasoning is used to reach the conclusion. Use Tools: Every day last week, Sally had a turkey sandwich for lunch. Sally will have a turkey sandwich for lunch today. What type of reasoning is used to reach the conclusion?

• Inductive reasoning

• Deductive reasoning