Madeline is asked to analyze the true statements shown. If two lines meet at a 90 degrees angle, they are perpendicular. If two lines are perpendicular, they have opposite reciprocal slopes. Which conclusion can Madeline draw from the given statements?
Answer
A
Based on inductive reasoning, if two lines have opposite reciprocal slopes, then they meet at a 90 degrees angle.
B
Based on the law of syllogism, if two lines have opposite reciprocal slopes, then they meet at a 90 degrees angle.
C
Based on inductive reasoning, if two lines meet at a 90 degrees angle, then they have opposite reciprocal slopes.
D
Based on the law of syllogism, if two lines meet at a 90 degrees angle, then they have opposite reciprocal slopes.
Explanation
Let p mean the lines meet at a 90-degree angle, and let r mean their slopes are opposite reciprocals. The statements give p → perpendicular and perpendicular → r, so the law of syllogism gives p → r. Therefore, if two lines meet at a 90-degree angle, they have opposite reciprocal slopes, as stated in choice D.
AI-written and checked against the verified answer.