Use deductive reasoning to form a valid conclusion from the given statements. State the law of logic that you applied to form such conclusion.
1. If two points of a line lie on a plane, then the line also lies on a plane.
Points A and B lie on plane M.
Conclusion:
Law of logic:.
2.Complements of congruent angles are congruent.
Angles 1 and 2 are complementary angles
Angles 2 and 3 are complementary angles.
Conclusion:
Law of logic:
3. If angles A and B are vertical, then angles A and B are congruent.
If angles A and B are congruent, then their measures are equal.
Conclusion:
Law of logic:
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Answer:
9. What conclusion can be obtained from the given statements?
If two planes intersect, then their intersection is a line.
Planes S and R intersect.
a. Planes S and R intersect at a line by the Law of Syllogism.
b. Planes S and R intersect at a point by the Law of Syllogism.
c. Planes S and R intersect at a line by the Law of Detachment
d. Planes S and R intersect at a point by the Law of Detachment.
19. What conclusion can be deduced from the following arguments?
Any three distinct noncollinear points lie on exactly one plane.
Points P and Q lie on line 1. Point R does not lie on line 1.
a. Points P, Q, and R lie on line 1.
b. Points P, Q, and R are collinear.
c. Points P, Q, and R are coplanar.
d. Points P, Q, and R are noncoplanar.
20. What conclusion can be drawn from the following arguments?
If two distinct planes intersect, their intersection is a line.
Planes P and M are distinct planes that intersect.
Point R lies on both planes P and M.
Point S lies on both planes P and M.
a. Points R and S determine a line.
b. The intersection of planes P and M is RS.
c. Point R is the intersection of planes P and M.
d. Point S is the intersection of planes P and M.
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