# Question Video: Applying Properties of Similarity Mathematics • 8th Grade

The figure shows two triangles: 𝐴𝐵𝐶 and 𝐴′𝐵′𝐶′: Work out the measure of angle 𝐴𝐵𝐶. What does the AA criterion tell us about these two triangles?

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### Video Transcript

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.