Given that triangle 𝐴𝐵𝐶 is
congruent to triangle 𝑋𝑌𝑍, find the measure of angle 𝐵.
Because we’re told that these two
triangles are congruent, that means that they will have pairs of corresponding
angles congruent. What we need to do here is to work
out exactly which angles are congruent. Sometimes, it can be very easy to
tell from a diagram and other times not quite so easy. But we can use the order of the
letters to help us.
As we’re told that triangle 𝐴𝐵𝐶
is congruent to triangle 𝑋𝑌𝑍, that means that the angle at 𝐴 is corresponding
with the angle at 𝑋. So, both the angle at 𝐴 and the
angle at 𝑋 will be 54 degrees. In the same way, this angle 𝐵 in
triangle 𝐴𝐵𝐶 is corresponding to the angle 𝑌 in triangle 𝑋𝑌𝑍. And both of these will be 52
degrees. As we were asked to find the
measure of angle 𝐵, then our answer would be that this is 52 degrees.
For completeness, we can note that
the angle at 𝐶 would be corresponding to the angle at 𝑍. And these would both be 74
degrees. But as we’re asked for 𝐵, that’s