### Video Transcript

Given that the measure of angle
πΉπΆπ΄ equals 134 degrees in the figure below, two sides are equal. Which are these?

We can begin this problem by adding
the extra angle information to the diagram, namely, that we have a second angle
measure of 134 degrees, which is the measure of angle πΉπΆπ΄. We can also observe that in this
figure we have three parallel line segments. They are π·πΈ, πΆπΉ, and π΄π΅. We should be able to identify some
other angle measures by using the properties of parallel lines and transversals. Firstly, we can determine that
angles π΅π·πΈ and π·π΅π΄ are supplementary, as they are contained within the two
parallel lines and the transversal π΅π·. These two angles must add to give
180 degrees. Therefore, to find the measure of
angle π·π΅π΄, we subtract 134 degrees from 180 degrees, which gives us an angle
measure of 46 degrees.

Then, we can identify another pair
of supplementary angles. This time, considering the parallel
lines πΆπΉ and π΄π΅, we note that angles πΉπΆπ΄ and πΆπ΄π΅ are also
supplementary. So, to find the measure of angle
πΆπ΄π΅, we subtract 134 degrees from 180 degrees. And we already know that this will
give us a value of 46 degrees.

We can now consider the question
regarding which two sides are equal. Well, we might not immediately
notice anything about the sides. However, we have worked out that
there are two congruent angles. And if we consider these angles as
part of the triangle π΄π΅πΆ, then these two congruent angles tell us something about
the type of triangle that it is.

By the converse of the isosceles
triangle theorem, we know that if two angles in a triangle are congruent, then the
sides opposite those angles are congruent. And by definition, we have an
isosceles triangle. So, the two congruent sides are
π΄πΆ and π΅πΆ. Therefore, we can give the answer
that it is side length π΄πΆ and side length π΅πΆ that are equal.