Question

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look at the diagram.
which term describes \\(\overline{bd}\\)?
perpendicular bisector
altitude
median
none of these

Explanation:

Step1: Recall definitions

• Perpendicular bisector: A line that is perpendicular to a segment and bisects it (cuts it into two equal parts at a right angle).
• Altitude: A perpendicular segment from a vertex to the line containing the opposite side.
• Median: A segment from a vertex to the midpoint of the opposite side (bisects the opposite side into two equal lengths).

Step2: Analyze the diagram

From the diagram, \( AD = DC = 64 \), so \( D \) is the midpoint of \( AC \). The segment \( \overline{BD} \) connects vertex \( B \) to the midpoint \( D \) of side \( AC \).

Step3: Match with definitions

• It's not necessarily a perpendicular bisector (no indication of right angle).
• It's not an altitude (no indication of perpendicularity to \( AC \)).
• It is a median because it connects a vertex to the midpoint of the opposite side.

Answer:

median