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NAME
2-4
DATE
PERIOD
Skills Practice
Deductive Reasoning
Determine whether the stated conclusion is valid based on the given information.
If not, write invalid. Explain your reasoning.
1. Given: If the sum of the measures of two angles is 180, then the angles are
supplementary. m∠ A + m∠ B is 180.
Conclusion: ∠ A and ∠ B are supplementary.
Valid; The hypothesis of the conditional is true, therefore the conclusion is true.
2. Given: If the sum of the measures of two angles is 90, then the angles are
complementary. m∠ ABC is 45 and m∠ DEF is 48.
Conclusion: ∠ ABC and ∠ DEF are complementary.
The hypothesis of the conditional statement is not true, so we do not know if
the conclusion is true.
3. Given: If the sum of the measures of two angles is 180, then the angles are
supplementary. ∠1 and ∠2 are a linear pair.
Conclusion: ∠1 and ∠2 are supplementary.
Use the Law of Syllogism to draw a valid conclusion from each set of statements,
if possible. If no valid conclusion can be drawn write no valid conclusion and
explain your reasoning.
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.
If two angles are complementary, 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.
If the heat wave continues, then energy costs will be higher.
6. If it is Tuesday, then Marla tutors chemistry.
If Marla tutors chemistry, then she arrives home at 4 P.M.
If it is Tuesday, then Marla arrives home at 4 P.M.
7. If a marine animal is a starfish, then it lives in the intertidal zone of the ocean.
The intertidal zone is the least stable of the ocean zones.
If a marine animal is a starfish, then it lives in the least stable of the
ocean zones.
Chapter 2
27
Glencoe Geometry
Lesson 2-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
If ∠1 and ∠2 are a linear pair, then the sum of their measures is 180.
Thus, the hypothesis of the conditional is true, and therefore the
conclusion is true.