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.

A. Based on the law of syllogism, if two lines meet at a 90 angle, then they have opposite reciprocal slopes.
B. Based on the law of syllogism, if two lines have opposite reciprocal slopes, then they meet at a 90 angle.
C. Based on inductive reasoning, if two lines meet at a 90 angle, then they have opposite reciprocal slopes.
D. Based on inductive reasoning, if two lines have opposite reciprocal slopes, then they meet at a 90 angle.

Answer 1

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

Explanation:

Law of Syllogism which is also known as reasoning by transitivity is a valid argument method of a deductive reasoning that follows a sequence.

Its similar to the transitive property of equality, which states that if a=b and b=c then a=c

The given statement : If two lines meet at a 90 angle, they are perpendicular. If two lines are perpendicular, they have opposite reciprocal slopes.

let a →" two lines meet at a 90 angle"

b→ "two lines are perpendicular are perpendicular"

c→" two lines have opposite reciprocal slopes"

Since a→b and b→c

Therefore by law of syllogism, a→c

i.e. If two lines meet at a 90 angle, then they have opposite reciprocal slopes.