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.

Answer 1

Angles ABC and DBE are congruent.

Answer 2

A) Angles ABC and DBE are congruent.

Explanation:

Let's see Law of Detachment

There will be two statements. If the two statements are true, then we can conclude another statement that is true.

i) If p , then q

ii) p

Conclusion : q

For example:

i) If it is rains, then I will get an umbrella.

ii) If it is rains,

Conclusion: I will get an umbrella.

We are given the following statement.

i) If two angles are vertical, then they are congruent.

ii) Angles ABC and DBE are vertical.

Conclusion: Angles ABC and DBE are congruent.

Therefore, answer is A) Angles ABC and DBE are congruent.