Question

in ⊙o if \\(\overline{gs} \perp \overline{xj}\\) and \\(\overline{xj} \perp \overline{ea}\\), what is true about \\(\overline{gs}\\) and \\(\overline{ea}\\) ?

Explanation:

Step1: Recall the property of perpendicular lines

If two lines are both perpendicular to the same line, then they are parallel to each other.

Step2: Apply the property to the given lines

We know that \(\overline{GS} \perp \overline{XJ}\) and \(\overline{XJ} \perp \overline{EA}\). So, by the property of perpendicular lines (if \(a\perp c\) and \(b\perp c\), then \(a\parallel b\)), we can conclude that \(\overline{GS}\parallel\overline{EA}\).

Answer:

\(\boldsymbol{\overline{GS}\parallel\overline{EA}}\) (the option " \(\overline{GS}\parallel\overline{EA}\)")