Page 187 - Math Course 2 (Book 2)

Deductive Reasoning

Skill Practice!

Determine whether the stated conclusion is valid based on the given information.
If not, write invalid. Explain your reasoning.
If the sum of the measures of two angles is 180, then the angles are supplementary.

1. Given: m∠A + m∠B is 180.
Conclusion: ∠A and ∠B are supplementary.

2. Given: m∠ABC is 95 and m∠DEF is 90.
Conclusion: ∠ABC and ∠DEF are supplementary.

3. Given: ∠1 and ∠2 are a linear pair.
Conclusion: ∠1 and ∠2 are supplementary.

Use the Law of Syllogism to determine whether a valid conclusion can be reached from each set of
statements. If a valid conclusion is possible, write it.

4. If two angles are complementary, then the sum of their measures is 90.
If the sum of the measures of two angles is 90, then both of the angles are acute.

5. If the heat wave continues, then air conditioning will be used more frequently.
If air conditioning is used more frequently, then energy costs will be higher.

Determine whether statement (3) follows from statements (1) and (2) by the Law of Detachment or the Law of
Syllogism. If it does, state which law was used. If it does not, write invalid.
6. (1) If it is Tuesday, then Marla tutors chemistry.
(2) If Marla tutors chemistry, then she arrives home at 4 P.M.
(3) If Marla arrives at home at 4 P.M., then it is Tuesday.

7. (1) If a marine animal is a starfish, then it lives in the intertidal zone of the ocean.
(2) The intertidal zone is the least stable of the ocean zones.
(3) If a marine animal is a starfish, then it lives in the least stable of the ocean zones.

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