In this exercise we want to identify segment BD as an altitude, median or perpendicular bisector. Let's start by recalling the definitions of these three concepts.
Name
Definition
Altitude
An altitude is a segment from a vertex to the line containing the opposite side and perpendicular to the line containing that side.
Median
A median of a triangle is a segment with endpoints being a vertex of a triangle and the midpoint of the opposite side.
Perpendicular Bisector
A perpendicular bisector is a segment bisector that is also perpendicular to this segment.
Now let's consider the triangle marked in the picture.
On the diagram we are given that segments AD and DC are congruent. Together they form the segment AC. Therefore, D is a midpoint of AC. We conclude that BD is a median of â–ł ABC, because it connects a vertex of a triangle with the midpoint of the opposite side.
