Video Transcript
In the given figure, triangle
๐ด๐ต๐ถ and ๐ต๐ถ๐ท have two equal sides and share one equal angle. Are triangles ๐ด๐ต๐ถ and ๐ต๐ถ๐ท
congruent?
Letโs start by highlighting our
triangles. We have the slightly larger
triangle ๐ด๐ต๐ถ and then we have this slightly smaller triangle marked in orange,
๐ต๐ถ๐ท. As we can clearly see, these are
different sizes and therefore would not be congruent. But as we indeed can see, we do
have some corresponding sides of equal length. And we do have a corresponding
angle of equal length. Perhaps we find some sort of
problem with the congruency rules. So letโs note down what we know
about each triangle and see if we can work out whatโs happening.
We can see in our diagram that we
have two lengths marked as two units, the length ๐ด๐ต and the length ๐ต๐ท, which we
could then write as congruent. The line ๐ต๐ถ of length four occurs
in both triangles. Finally, we can see that we have a
common angle. The angle ๐ด๐ถ๐ต would be equal to
the angle ๐ต๐ถ๐ท. It might be tempting then to say
that we have a congruency because of a real SSA. But in fact, this is not a
congruency rule. Because as we can see from our
diagram, we could in fact create two noncongruent triangles using two corresponding
pairs of sides congruent and a pair of corresponding angles congruent.
We could have used the congruency
rule SAS if the angle was included between the two sides. But itโs not in this diagram. So therefore, we can happily say
that our two triangles are not congruent. They didnโt look congruent. And even in the case of a badly
drawn diagram, we canโt prove that theyโre congruent.
