### Video Transcript

Using the diagram, which of the
following is equal to π΄π΅ over π΄π·? (A) π΄π΅ over π·π΅, (B) π΄πΆ over
π΄πΈ, (C) π΄πΆ over πΈπΆ, (D) π΄π· over π·π΅, or (E) π΄πΈ over πΈπΆ.

In our diagram, line segment πΈπ·
is parallel to line segment πΆπ΅. Because of that, we have two
similar triangles. We can say that triangle π΄πΈπ· is
similar to triangle π΄πΆπ΅. And in similar triangles,
corresponding side lengths are proportional. Weβre interested in the ratio π΄π΅
over π΄π·. π΄π΅ represents a larger side
length, and π΄π· is the corresponding smaller side length. This means that we are looking for
the ratio that has a larger side length and the corresponding smaller side
length.

Option (A) has π΄π΅ corresponding
to π·π΅. But π·π΅ is not part of the smaller
triangle, which means option (A) cannot work. Option (B) has side length π΄πΆ,
which is part of our larger triangle, and then the distance from π΄ to πΈ. π΄ to πΈ is the corresponding
smaller side length from π΄πΆ. This is an equal ratio. But letβs check the others just in
case.

Again, we have the side length
π΄πΆ, but the denominator is πΈπΆ. And πΈπΆ is not part of the smaller
triangle, which makes this an invalid ratio. What about option (D)? π΄π· is a smaller side length, and
then π·π΅, which is not part of our similar triangles. And we see that again π΄πΈ is a
smaller triangle, but πΈπΆ is not part of any of our similar triangles. The only ratio that is equal to
π΄π΅ over π΄π· in this list is π΄πΆ over π΄πΈ.