### Video Transcript

Which congruence criteria can be
used to prove that the two triangles in the given figure are congruent? Option (A) SSS, option (B) SAS,
option (C) ASA.

In this question, weโre asked for a
congruence criteria. If we look at the options here, we
can see that the S refers to side and the A represents angle. So, letโs look at our two
triangles, ๐ด๐ต๐ถ on the left and triangle ๐ธ๐ท๐น on the right. Weโll make a note of any
corresponding pairs of angles or sides which are congruent.

In triangle ๐ด๐ต๐ถ, we can see that
this angle ๐ด๐ต๐ถ is marked as 104 degrees. The same is true of angle ๐ธ๐ท๐น in
triangle ๐ธ๐ท๐น. Therefore, we could say that these
two angles are congruent. We can see that angle ๐ด๐ถ๐ต is
22.8 degrees and so is angle ๐ธ๐น๐ท. So, we have another pair of
congruent angles. We can see that there are two sides
which are marked as 7.1, side ๐ด๐ถ on triangle ๐ด๐ต๐ถ and side ๐ธ๐น on triangle
๐ธ๐ท๐น. Therefore, these sides are
congruent.

What weโve shown here is that we
have angle-angle-side, so we could use the angle-angle-side rule to prove
congruence. We could say that triangle ๐ด๐ต๐ถ
and triangle ๐ธ๐ท๐น are congruent using the AAS rule.

A quick reminder that the order of
letters is important when describing congruence. For example, we know that angle ๐ถ
in triangle ๐ด๐ต๐ถ is congruent with angle ๐น in triangle ๐ธ๐ท๐น. We know that angle ๐ต and angle ๐ท
are congruent, and angle ๐ด and ๐ธ are congruent. So, when we look at the answer
options, we see a problem. The AAS rule is not listed as an
option. So, letโs see if we could prove
congruence using another rule too.

We donโt know any additional
information about the length of the sides. So, letโs have a look at the
angles. If we look at angle ๐ต๐ด๐ถ in the
first triangle and angle ๐ท๐ธ๐น in the second triangle, we could actually work out
the value of these angles by subtracting 104 and 22.8 from 180 degrees, as we know
that there are 180 degrees in total in the triangle. So, both of these angles would be
equal to each other; theyโre congruent.

Weโve also just proved that these
two triangles are congruent. Therefore, we know that these third
angles must also be congruent. So therefore, if we take into
account these last three pieces of information, we have two angles and the included
side. Therefore, we have the ASA
rule. So, weโve shown that these
triangles are congruent using the ASA rule as well, which was the answer given in
option (C).