Question

katie 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? choose three correct answers. her conclusion is true. she used the law of detachment. her conclusion is valid. she used inductive reasoning. the statements can be represented as \if p, then q and if q then r.\

Explanation:

The law of detachment states that if a conditional statement "if p, then q" is true and p is true, then q is true. Here, the conditional is "if two lines are perpendicular, then they intersect at a right - angle" (p: two lines are perpendicular, q: they intersect at a right - angle) and it's given that lines A and B are perpendicular (p is true), so the conclusion that they intersect at a right - angle (q is true) is valid and true. Inductive reasoning is not used as it involves making generalizations from specific examples, while this is a case of deductive reasoning using the law of detachment. The statements cannot be represented as "if p, then q and if q then r" as there is only one conditional and one given fact.

Answer:

1. Her conclusion is true.
2. She used the law of detachment.
3. Her conclusion is valid.