Question

consider the diagram. which line segment has the same measure as \\(\overline{tq}\\)? \\(\bigcirc\\ \overline{sr}\\) \\(\bigcirc\\ \overline{tr}\\) \\(\bigcirc\\ \overline{st}\\) \\(\bigcirc\\ \overline{qs}\\)

Explanation:

Step1: Analyze the Diagram

The diagram shows a line \( m \) (with points \( S \) and \( T \)) perpendicular to segment \( QR \), bisecting it (marked with equal segments). This suggests symmetry about line \( m \).

Step2: Identify Congruent Segments

In a symmetric figure with a perpendicular bisector, segments from a point on one side to the bisected segment's endpoints should be congruent. So, \( \overline{TQ} \) and \( \overline{TR} \) should be congruent (same measure) due to the perpendicular bisector property.

Answer:

B. \(\overline{TR}\)