Question

name the special segment for the following pictures.
\\( \overline { a c } \\)
\\( \overline { h e } \\)
\\( \overline { j l } \\)
\\( \overline { p n } \\)

Explanation:

• For \(\overline{AC}\): In a triangle, a median is a segment that connects a vertex to the mid - point of the opposite side. Since \(C\) is the mid - point of \(BF\) (as indicated by the tick marks), \(\overline{AC}\) is a median.
• For \(\overline{HE}\): A perpendicular bisector of a segment is a line (or segment) that is perpendicular to the segment and passes through its mid - point. Here, \(HE\) is perpendicular to \(DF\) and \(E\) is the mid - point of \(DF\) (shown by tick marks), so \(\overline{HE}\) is a perpendicular bisector.
• For \(\overline{JL}\): An angle bisector is a segment that divides an angle into two equal parts. In \(\triangle IJK\), \(\overline{JL}\) divides \(\angle IJK\) into two equal angles (as indicated by the arc markings), so \(\overline{JL}\) is an angle bisector.
• For \(\overline{PN}\): An altitude is a segment from a vertex of a triangle perpendicular to the opposite side (or its extension). In \(\triangle MON\), \(\overline{PN}\) is perpendicular to \(MO\), so \(\overline{PN}\) is an altitude.

Answer:

\(\overline{AC}\): Median, \(\overline{HE}\): Perpendicular bisector, \(\overline{JL}\): Angle bisector, \(\overline{PN}\): Altitude