Video Transcript
True or False: In the given figure,
the line segment that is passing through points 𝐵 and 𝐷 is also passing through
point 𝐶.
In this question, we are given a
figure that contains three points 𝐵, 𝐶, and 𝐷 that are connected by a straight
line. We need to determine if a line
segment that passed through 𝐵 and 𝐷 must also pass through 𝐶.
We can start by recalling that a
line segment is a finite section of a straight line between two points. We call these the endpoints of the
line segment. And the line segment is the set of
all points that lie on this finite section of line. For example, if we have two points
𝑃 and 𝑄, then the line segment between 𝑃 and 𝑄 contains all of the points on the
finite section of line between the two points, including both 𝑃 and 𝑄. We represent line segments using an
overline over its endpoints.
If we look at the given figure, we
can see that the line segment stops at 𝐵 and 𝐷, so these are its endpoints. Therefore, this is the line segment
between 𝐵 and 𝐷, and it includes every point on this finite section of line
between 𝐵 and 𝐷. We can see in the diagram that 𝐶
lies on this section of line. So 𝐶 lies on the line segment
between 𝐵 and 𝐷. Hence, it is true that in the
figure the line segment passing through 𝐵 and 𝐷 also passes through 𝐶.
