### Video Transcript

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

We see from the diagram that
the base of triangle π΄πΈπ·, thatβ²s side πΈπ·, is parallel to the base of
triangle π΄π΅πΆ, thatβ²s side πΆπ΅. Since corresponding angles must
be equal if the two lines are parallel, angle π·πΈπ΄ is equal to angle π΅πΆπ΄,
and angle πΈπ·π΄ is equal to angle πΆπ΅π΄. Then side πΈπ· creates triangle
π΄π·πΈ, which is similar to the larger triangle π΄π΅πΆ. Since these triangles are
similar, the ratios of their corresponding side lengths must be equal. In particular, π΄πΈ over π΄πΆ
is equal to π΄π· over π΄π΅.

Now we want to find which of
the given fractions is equal to π΄π΅ over π΄π·. And we can do this by finding
the reciprocal of both sides of our equation, which gives us π΄πΆ over π΄πΈ is
equal to π΄π΅ over π΄π·. Hence, π΄π΅ over π΄π· is equal
to π΄πΆ over π΄πΈ, which corresponds to the given option (D).