Using the given figure, determine
whether the following is true or false. The line segment that is passing
through points 𝐵 and 𝐷 is also passing through point 𝐶.
In order to answer this question,
we’re going to need to recall what we actually mean by a line segment. A line segment is a part of a line,
and that part is bounded by two distinct endpoints. We’re told that our line segment
passes through points 𝐵 and 𝐷. In fact, its two endpoints, as we
can see from the diagram, are 𝐵 and 𝐷. So we represent it as shown. It’s 𝐵𝐷 with a line above it.
So let’s compare point 𝐶 to points
𝐵 and 𝐷. It sits on the line passing through
these points and halfway roughly between points 𝐵 and 𝐷, halfway between the
endpoints of the line segment. By definition, a line segment must
be straight and contain every point on the line between its endpoints. So we can say this is true. The line segment 𝐵𝐷 passes
through point 𝐶.