### Video Transcript

π and π are planes that intersect
at line πΏ. π΅ is a point on plane π, and πΆ
is a point on plane π. Determine the intersection of plane
π with plane π΄π΅πΆ.

In our figure, we can see line πΏ
is the intersections of plane π and π. We want the intersection of plane
π with plane π΄π΅πΆ. Letβs first identify plane π. We can see that the plane π
includes the points π΄ and πΆ. And if weβre interested in plane
π΄π΅πΆ, we recognize that the points π΄ and π΅ are located along the same plane,
plane π, and the points πΆ and π΄ are both located in the plane π. This tells us that the point π΄ is
located in plane π and in plane π.

Because the points π΄, π΅, and πΆ
are noncolinear, they can form exactly one plane. To see plane π΄π΅πΆ, first, weβll
connect a line through points π΄ and π΅ and another line through the points π΄,
πΆ. From there, we can add an
additional line that goes through point πΆ. By connecting these lines, we have
some idea of how this plane would look.

At this point, we should start to
see that the plane π΄π΅πΆ is slicing through the plane π. And this slicing is happening along
the line that goes through the points π΄ and πΆ. Plane π contains the line π΄πΆ, as
does plane π΄π΅πΆ, which makes the intersection of plane π and plane π΄π΅πΆ the
line π΄πΆ.