Question

if points n, u, and t are collinear, name all the segments they determine.

□(overline{tu})
□(overline{nu})
□(overline{tn})
□(overline{nt})
□(overline{ut})
□(overline{un})

Explanation:

Step1: Recall segment - naming rule

A line - segment is named by its two endpoints. Given three collinear points \(N\), \(U\), and \(T\), we form segments by taking pairs of these points.

Step2: List all possible pairs

The possible pairs of endpoints are \((N,U)\), \((N,T)\), and \((U,T)\). The segments are \(\overline{NU}\), \(\overline{NT}\), \(\overline{UT}\). Also, \(\overline{UN}\), \(\overline{TN}\), \(\overline{TU}\) represent the same segments respectively.

Answer:

\(\overline{NU}\), \(\overline{TN}\), \(\overline{NT}\), \(\overline{UT}\), \(\overline{TU}\), \(\overline{UN}\)