Question

1. what type of segment is \\(\overline{tr}\\) in the diagram below?

(diagram of a triangle with vertices t, q, s; r is on qs, qr = 8 cm, rs = 8 cm, tq = 15 cm, ts = 14 cm, and segment tr drawn from t to r)

Explanation:

Step1: Analyze the triangle's base

The base \( QS \) is divided into \( QR = 8 \, \text{cm} \) and \( RS = 8 \, \text{cm} \), so \( R \) is the midpoint of \( QS \).

Step2: Identify the segment type

A segment from a vertex to the midpoint of the opposite side is a median. Since \( T \) is a vertex and \( R \) is the midpoint of \( QS \), \( \overline{TR} \) connects vertex \( T \) to the midpoint of side \( QS \).

Answer:

Median (specifically, the median of triangle \( TQS \) from vertex \( T \) to side \( QS \))