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
\\( \overline { h n } \\)
\\( \overline { q p } \\)
\\( \overline { f k } \\)
\\( \overline { q k } \\)
\\( \overline { l m } \\)
\\( \overline { e f } \\)
\\( \overline { j h } \\)

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 divides it into two equal - length parts.

Step2: Analyze each segment

• For \(\overline{LM}\):

Since \(M\) is the mid - point of the side (as indicated by the tick marks) and \(\overline{LM}\) is perpendicular to the side (right - angle symbol at \(M\)), \(\overline{LM}\) is a perpendicular bisector.

• For \(\overline{FK}\):

\(K\) is the mid - point of the side (tick marks) and \(\overline{FK}\) is perpendicular to the side (right - angle symbol at \(K\)), so \(\overline{FK}\) is a perpendicular bisector.

• For \(\overline{QK}\):

\(K\) is the mid - point of the side (tick marks) and \(\overline{QK}\) is perpendicular to the side (right - angle symbol at \(K\)), so \(\overline{QK}\) is a perpendicular bisector.

• For \(\overline{HN}\):

There is no indication that \(N\) is the mid - point of a side.

• For \(\overline{QP}\):

There is no indication that \(P\) is the mid - point of a side.

• For \(\overline{EF}\):

There is no indication that \(E\) is the mid - point of a side.

• For \(\overline{JH}\):

There is no indication that \(H\) is the mid - point of a side.

Answer:

\(\overline{LM}\), \(\overline{FK}\), \(\overline{QK}\)