Question

given the following statements, what conclusion can be drawn using the law of detachment? if two angles are vertical, then they are congruent angles abc and dbe are vertical angles abc and dbe are congruent. no conclusion can be reached based on the law of detachment angles abc and dbe are not congruent. angle abc is a counterexample.

Explanation:

The law of detachment states that if \(p
ightarrow q\) (if \(p\) then \(q\)) is a true conditional statement and \(p\) is true, then \(q\) is true. Here, \(p\) is “two angles are vertical” and \(q\) is “they are congruent”. Since angles \(ABC\) and \(DBE\) are vertical (\(p\) is true for these angles), by the law of detachment, \(q\) (they are congruent) must be true for these angles.

Answer:

Angles \(ABC\) and \(DBE\) are congruent.