Question

use the law of detachment to make a valid conclusion in the true situation.
a. if two segments have the same length, then they are congruent. bc = xy.

Explanation:

Step1: Identify the hypothesis and conclusion

The conditional statement is "If two segments have the same length, then they are congruent". The hypothesis \(p\) is "two segments have the same length" and the conclusion \(q\) is "they are congruent". We are given that \(BC = XY\), which means the segments \(BC\) and \(XY\) have the same length (satisfying the hypothesis).

Step2: Apply the Law of Detachment

The Law of Detachment states that if \(p
ightarrow q\) is a true conditional statement and \(p\) is true, then \(q\) is true. Since the conditional statement is true and the hypothesis (segments having the same length) is true for segments \(BC\) and \(XY\), we can conclude that the segments are congruent.

Answer:

Segment \(BC\) is congruent to segment \(XY\) (written as \(BC\cong XY\))