Question

madeline is asked to analyze the true statements shown. if two lines meet at a 90° angle, they are perpendicular. if two lines are perpendicular, they have opposite reciprocal slopes. which conclusion can madeline draw from the given statements? based on inductive reasoning, if two lines meet at a 90° angle, then they have opposite reciprocal slopes. based on the law of syllogism, if two lines have opposite reciprocal slopes, then they meet at a 90° angle. based on inductive reasoning, if two lines have opposite reciprocal slopes, then they meet at a 90° angle. based on the law of syllogism, if two lines meet at a 90° angle, then they have opposite reciprocal slopes.

Explanation:

Step1: Identify logical reasoning type

We have two statements: "If two lines meet at a 90° angle, they are perpendicular" and "If two lines are perpendicular, they have opposite reciprocal slopes". The law of syllogism combines two conditional statements where the conclusion of one is the hypothesis of the other.

Step2: Apply law of syllogism

Let \(p\) be "two lines meet at a 90° angle", \(q\) be "they are perpendicular" and \(r\) be "they have opposite reciprocal slopes". We have \(p
ightarrow q\) and \(q
ightarrow r\). By the law of syllogism \(p
ightarrow r\), which means if two lines meet at a 90° angle, then they have opposite reciprocal slopes.

Answer:

Based on the law of syllogism, if two lines meet at a 90° angle, then they have opposite reciprocal slopes.