Question

which conclusion can be drawn based on the true statements shown? if a line segment is a diameter, then it is the longest chord in a circle. line segment ab is a diameter. based on the law of syllogism, line segment ab is the longest chord in a circle. based on the law of detachment, line segment ab is the longest chord in a circle. based on the law of syllogism, the longest chord in a circle is a diameter. based on the law of detachment, the longest chord in a circle is a diameter.

Explanation:

Step1: Recall law of detachment

The law of detachment states if \(p
ightarrow q\) is true and \(p\) is true, then \(q\) is true. Here \(p\) is "a line - segment is a diameter" and \(q\) is "it is the longest chord in a circle", and we know \(p
ightarrow q\) is true and \(p\) (line segment \(AB\) is a diameter) is true.

Step2: Apply the law

By the law of detachment, we can conclude that \(q\) is true for line - segment \(AB\).

Answer:

Based on the law of detachment, line segment AB is the longest chord in a circle.