Question

madeline is asked to analyze the true statements shown.
if two lines meet at a $90^\circ$ 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 the law of syllogism, if two lines meet at a $90^\circ$ 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 $90^\circ$ angle.
based on inductive reasoning, if two lines meet at a $90^\circ$ angle, then they have opposite reciprocal slopes.
based on inductive reasoning, if two lines have opposite reciprocal slopes, then they meet at a $90^\circ$ angle.

Explanation:

1. First, identify the logical structure: The given statements are a chain:

• Statement 1: If lines meet at $90^\circ$, then they are perpendicular.
• Statement 2: If lines are perpendicular, then they have opposite reciprocal slopes.

1. The law of syllogism allows combining two conditional statements $P

ightarrow Q$ and $Q
ightarrow R$ into $P
ightarrow R$. Here, $P$ = "lines meet at $90^\circ$", $Q$ = "lines are perpendicular", $R$ = "lines have opposite reciprocal slopes", so we get $P
ightarrow R$.

1. Inductive reasoning uses specific examples to make generalizations, which is not the case here; this is deductive reasoning via syllogism.
2. The reverse statement (starting with opposite reciprocal slopes) is not supported by the given chain of statements.

Answer:

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