Question

given \\( \overline { g e } \cong \overline { p e } \\), select all segments below in the triangle that are perpendicular bisectors. hint: there are 3 perpendicular bisectors

Explanation:

Step1: Recall the definition of perpendicular bisector

A perpendicular bisector of a segment is a line (or segment) that is perpendicular to the segment and bisects (divides into two equal parts) it.

Step2: Analyze each segment

• For segment \(LM\): It is perpendicular to \(GH\) and bisects \(GH\) (marked with equal - length ticks), so \(LM\) is a perpendicular bisector.
• For segment \(FQ\): It is perpendicular to \(GP\) (marked with a right - angle symbol) and since \(GE\cong PE\), and assuming the construction (from the properties of perpendicular bisectors in a triangle), \(FQ\) bisects \(GP\), so \(FQ\) is a perpendicular bisector.
• For segment \(HK\): It is perpendicular to \(NP\) (marked with a right - angle symbol) and bisects \(NP\) (marked with equal - length ticks), so \(HK\) is a perpendicular bisector.

Answer:

\(LM\), \(FQ\), \(HK\)