The figure shows two triangles,
𝐴𝐵𝐶 and 𝐴 prime 𝐵 prime 𝐶 prime. Work out the measure of angle
𝐴𝐵𝐶. What does the AA criterion tell
us about these two triangles?
In this question, we have two
triangles drawn on grid paper. And the first thing we’re asked
to do is find the measure of angle 𝐴𝐵𝐶, which is in the smaller triangle. In order to do this, we should
recall that the angles in a triangle add up to 180 degrees. We’ll therefore need to
calculate 180 degrees subtract the other two angles of 114.3 degrees and 34.1
degrees, which gives 31.6 degrees. And so that’s our answer for
the measure of angle 𝐴𝐵𝐶.
In the second part of this
question, we’re asked about the AA criterion, which is the criterion we use to
show that two triangles are similar. It’s what we have when we
demonstrate that there are two pairs of angles congruent. So, let’s have a closer look at
these two triangles. The angle 𝐴𝐵𝐶 that we’ve
just worked out as 31.6 degrees has a corresponding angle at angle 𝐴 prime 𝐵
prime 𝐶 prime of the same value, 31.6 degrees. We also have another pair of
corresponding congruent angles, the angle 𝐶 prime 𝐴 prime 𝐵 prime and angle
𝐶𝐴𝐵, which are both given as 34.1 degrees. Showing that there are two
pairs of corresponding congruent angles or the AA rule, we demonstrate that
these two triangles are similar.
We could therefore answer the
second part of this question with a statement such as this: as both triangles
share two angels of equal measures, they must be similar.