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:

First, clarify the two laws: The law of detachment applies when we have a conditional statement "If P, then Q" and we confirm P is true, so we conclude Q is true. The law of syllogism links two conditionals (If P then Q; If Q then R) to get If P then R. Here, we have "If a segment is a diameter (P), then it's the longest chord (Q)" and "AB is a diameter (P is true)". This matches the law of detachment, leading to the conclusion AB is the longest chord.

Answer:

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