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Reasoning and Writing of Proofs 1
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Choose your answer to each question.

1. What conclusion(s) can be formed from the given statements below?
Given: 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.
(a) Line AB lies on plane M.
(b) Line AB does not lie on plane M.
Both (a) and (b)
Neither (a) nor (b)
Answer: Line AB lies on plane M.
2. What law of logic did you apply to form a valid conclusion in the previous item?
Law of Detachment
Law of Syllogism
Answer: Law of Detachment
3. What conclusion(s) can be formed from the given statements below?
Given: Complements of congruent angles are congruent.
Angles 1 and 2 are complementary angles.
Angles 2 and 3 are complementary angles.
(a) Angles 1 and 3 are congruent.
(b) Angles 1 and 3 are complementary angles.
Both (a) and (b)
Neither (a) nor (b)
Answer: Angles 1 and 3 are congruent.
4. What law of logic did you apply to form a valid conclusion in the previous item?
Law of Detachment
Law of Syllogism
Answer: Law of Detachment
5. What conclusion(s) can be formed from the given statements below?
Given: If angles A and B are vertical angles, then angles A and B are congruent.
If angles A and B are congruent, then their measures are equal.
(a) If angles A and B are vertical angles, then their measures are equal.
(b) If the measures of angles A and B are equal, then they are vertical angles.
Both (a) and (b)
Neither (a) nor (b)
Answer: If angles A and B are vertical angles, then their measures are equal.
6. What law of logic did you apply to form a valid conclusion in the previous item?
Law of Detachment
Law of Syllogism
Answer: Law of Syllogism
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