Question

from the construction marks shown in the diagram, we can tell that \\(\overline{cd}\\) is

a perpendicular bisector of \\(\triangle abc\\)
an angle bisector of \\(\triangle abc\\)
an altitude of \\(\triangle abc\\)
a median of \\(\triangle abc\\)

Explanation:

Identify the construction steps

1. An arc is drawn with its center at vertex \(C\), intersecting the opposite side \(AB\) at two distinct points.
2. From each of these two intersection points on \(AB\), arcs of equal radii are drawn below \(AB\), intersecting each other.
3. A line is drawn from vertex \(C\) through this intersection point, crossing \(AB\) at point \(D\).

Determine the geometric property

This sequence of steps represents the standard compass-and-straightedge construction of a perpendicular line from a point \(C\) to a line segment \(AB\).
Since \(\overline{CD}\) passes through vertex \(C\) and is perpendicular to the opposite side \(AB\), it is by definition an altitude of \(\triangle ABC\).

Answer:

• a perpendicular bisector of \(\triangle ABC\)
• an angle bisector of \(\triangle ABC\)
• an altitude of \(\triangle ABC\) (Correct answer)
• a median of \(\triangle ABC\)