Page 185 - Math Course 2 (Book 2)
P. 185
Deductive Reasoning
The following is a true conditional. Determine (1) If Mel and his date eat at the Peddler
whether the conclusion is valid based on the given Steakhouse before going to the prom,
information. Explain your reasoning. If two seg- they will miss the senior march.
ments are congruent and the second segment is
congruent to a third segment, then the first seg- (2) The Peddler Steakhouse stays open until
ment is also congruent to the third segment. 10 P.M.
Given: UV ; WX ≅ RT There is no valid conclusion.
Conclusion: WX ≅ UV and UV ≅ RT While both statements may be
Answer true, the conclusion of each
The hypothesis states that UV is a segment and WX ≅ RT. statement is not used as the
hypothesis of the other.
According to the hypothesis
for the conditional, you must
have two pairs of congruent Analyze Conclusions
Answer segments. The given only has
one pair of congruent segments. Examples
Therefore, the conclusion is not
valid.
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
Determine Valid Conclusions From Two Conditionals was used. If it does not, write invalid.
Examples (1) If the sum of the squares of two sides of a
triangle is equal to the square of the third
side, then the triangle is a right triangle.
2
2
2
PROM (2) For △XYZ, (XY) + (YZ) = (ZX) .
Use the Law of Syllogism to determine whether a (3) △XYZ is a right triangle.
valid conclusion can be reached from each set of
statements. p: the sum of the squares of the two sides of a
triangle is equal to the square of the third side
q: the triangle is a right triangle
By the Law of Detachment, if p → q is true and p is
true, then q is also true.
Statement (3) is a valid
Answer conclusion by the Law of
(1) If Salline attends the prom, she will go with Detachment
Mark.
(1) If Ling wants to participate in the wrestling
(2) If Salline goes with Mark, Donna will go with competition, he will have to meet an extra
Albert. three times a week to practice.
(2) If Ling adds anything extra to his weekly
If Salline attends the prom,
Answer schedule, he cannot take karate lessons.
Donna will go with Albert.
(3) If Ling wants to participate in the wrestling
competition, he cannot take karate lessons.
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