### Video Transcript

In the given quadrilateral, ๐ด๐น
and ๐ต๐น have the same length and ๐ธ๐น and ๐ถ๐น have the same length. Which angle has the same measure as
angle ๐ด๐น๐ธ? Hence, are triangles ๐ด๐น๐ธ and
๐ต๐น๐ถ congruent? If yes, state which congruence
criterion proves this.

In this diagram, we can see that
thereโs a quadrilateral which has some triangles within it. Weโre told that there are some line
segments which have the same length. So itโs always worthwhile putting
this onto a diagram if theyโre not already marked. ๐ด๐น and ๐ต๐น are the same length
and ๐ธ๐น and ๐ถ๐น are the same length. In the second question, weโll look
at congruency. But the first question asks us
about angle measures. Which angle would be the same as
angle ๐ด๐น๐ธ? Weโre not given any angle
measurements in this diagram, but we should recall that angles which are vertically
opposite will be equal. So angle ๐ต๐น๐ถ would also be the
same measurement. And thatโs our answer for the first
part of the question.

In the second part of the question,
we need to check if triangles ๐ด๐น๐ธ and ๐ต๐น๐ถ are congruent. So letโs note down any sides or
angles that we know are congruent. We were told in the question that
๐ด๐น and ๐ต๐น are the same length. We have shown in the first part of
the question that we have two congruent angles, angle ๐ด๐น๐ธ and angle ๐ต๐น๐ถ. And we were told that sides ๐ธ๐น
and ๐ถ๐น are the same length.

And so, we have two pairs of
congruent sides equal and a pair of congruent angles. Importantly, the angle is included
between the two sides, which means that we can use the SAS congruency criterion. If the angle wasnโt included
between the two sides, then it wouldnโt be sufficient to show congruence. So our answer for this part of the
question is, yes, these two triangles are congruent, and we use the SAS
criterion.