### Video Transcript

True or False: In the given figure,
if the measure of angle π΅ is equal to the measure of angle πΆ and the line segment
between π΄ and π· is a bisector of angle π΄, then triangle π΄π΅π· is congruent to
triangle π΄π·πΆ.

In this question, we are given a
geometric figure and asked to determine if two triangles in the figure are
congruent, which means that they would have corresponding sides of the same length
and corresponding angles of the same measure. We can do this by considering the
congruency criteria for triangles. Letβs begin by adding the given
information onto the sketch.

First, we are told that the measure
of angles π΅ and πΆ are equal. Second, we are told that line
segment π΄π· bisects the angle at π΄. This means that it splits the angle
into two angles of equal measure as shown.

There are a few different ways to
consider the congruency of the two triangles. One way is to note that triangle
π΄π΅πΆ is isosceles since it has two angles of equal measure. We can then recall that the
isosceles triangle theorem tells us that the sides opposite the congruent angles in
an isosceles triangle have the same length. So, π΄π΅ is equal to π΄πΆ as
shown.

We have now shown that triangles
π΄π΅π· and π΄πΆπ· have two angles of equal measure and the included side of these
corresponding angles have the same length. This is enough to prove that the
two triangles are congruent using the angle-side-angle congruence criterion. Hence, the answer is true.