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 not congruent. angle abc is a counterexample. angles abc and dbe are congruent. no conclusion can be reached based on the law of detachment.

Explanation:

Step1: Recall law of detachment

The law of detachment states that if a conditional statement "if p, then q" is true and p is true, then q is true.

Step2: Identify p and q

The conditional statement is "If two angles are vertical, then they are congruent", so p = "two angles are vertical" and q = "they are congruent". We are given that angles ABC and DBE are vertical (p is true).

Step3: Apply the law

Since the conditional is true and p is true, q must be true. So angles ABC and DBE are congruent.

Answer:

Angles ABC and DBE are congruent.