Question

question 30

from the construction marks shown below, we can see that \\(\overline{nq}\\) is a(n)*

• angle bisector
• altitude
• transversal
• median

Explanation:

Analyze the construction marks

The construction arcs show the standard method for finding the perpendicular bisector of the segment \(LM\). Two intersecting arcs are drawn above and below the segment \(LM\) using the endpoints \(L\) and \(M\) as centers with equal radii. The line passing through these intersections crosses the segment \(LM\) at its midpoint.

Identify the role of point Q

The vertical construction line intersects the base \(LM\) at point \(Q\). Because this line is the perpendicular bisector of \(LM\), point \(Q\) is the midpoint of the segment \(LM\).

Classify the segment NQ

The segment \(\overline{NQ}\) connects the vertex \(N\) of \(\triangle LNM\) to the midpoint \(Q\) of the opposite side \(LM\). By definition, a line segment joining a vertex of a triangle to the midpoint of the opposite side is a median.

Answer:

• angle bisector
• altitude
• transversal
• median (Correct answer)