Question

kellie is given the following information if two lines are perpendicular, then they intersect at a right angle. lines a and b are perpendicular she concludes that lines a and b intersect at a right angle. which statements are true? check all that apply she used inductive reasoning. she used the law of detachment. her conclusion is valid. the statements can be represented as \if p, then q and if q, then r\ her conclusion is true.

Explanation:

• Law of Detachment: The law of detachment states that if \(p

ightarrow q\) (if two lines are perpendicular (\(p\)), then they intersect at a right - angle (\(q\))) and \(p\) (lines \(A\) and \(B\) are perpendicular) is true, then \(q\) (lines \(A\) and \(B\) intersect at a right - angle) is true. So, she used the law of detachment.

• Validity and Truth of Conclusion: Since the law of detachment is a valid form of logical reasoning and the given statements (the conditional statement about perpendicular lines and the fact that lines \(A\) and \(B\) are perpendicular) are such that the conclusion follows logically, her conclusion is valid and true.

• Inductive Reasoning: Inductive reasoning is based on patterns and observations of multiple cases. Here, it is a deductive (specifically using the law of detachment) reasoning, not inductive.
• Statement Representation: The statements are of the form \(p

ightarrow q\) (if two lines are perpendicular (\(p\)), then they intersect at a right - angle (\(q\))) and \(p\) (lines \(A\) and \(B\) are perpendicular), not \(p
ightarrow q\) and \(q
ightarrow r\).

Answer:

B. She used the law of detachment, C. Her conclusion is valid, E. Her conclusion is true.