Question

which of the following is the correct name for \\( \overline { l m } \\) in \\( \triangle a b c \\) below?
a. midsegment
b. angle bisector
c. altitude
d. perpendicular bisector

Explanation:

A midsegment of a triangle is a segment that connects the midpoints of two sides of the triangle. In the given triangle \( \triangle ABC \), since \( L \) is the midpoint of \( AB \) (as indicated by the tick marks) and \( M \) is the midpoint of \( BC \) (as indicated by the tick marks), \( \overline{LM} \) connects the midpoints of two sides.

• An angle bisector divides an angle into two equal parts. There is no indication that \( \overline{LM} \) divides any angle.
• An altitude is a perpendicular segment from a vertex to the opposite side. There is no indication of perpendicularity.
• A perpendicular bisector is a line that is perpendicular to a segment and bisects it. There is no indication that \( \overline{LM} \) is perpendicular to any side.

Answer:

A. Midsegment