Video Transcript
Are these two triangles similar?
Let’s start this question by recalling that similar triangles have corresponding pairs of angles congruent and corresponding pairs of sides in proportion. There are a number of different criterion that we can use to check or prove if two triangles are similar. As we’re not given any side length measurements here, it might be sensible to check if the AA or angle-angle criterion applies here. For this rule, we need to see if there are two pairs of corresponding angles congruent. In the diagrams, we have a pair of corresponding angles of 55 degrees. However, the other two angles that we’re given in these triangles are not congruent.
Let’s then see if we can work out the missing angle in each triangle. We should remember that the angles in a triangle sum to 180 degrees. So to find the missing angle in the triangle on the left, we need to calculate 180 degrees subtract 55 degrees plus 54 degrees. 55 plus 54 gives us 109 degrees. So subtracting that from 180 degrees gives us 71 degrees. So the first missing angle is 71 degrees. Using the same approach on the triangle on the right, we calculate 180 degrees subtract 55 degrees plus 70 degrees, which leaves us with a missing angle of 55 degrees.
In order to check, therefore, if the AA rule applies, we need to have two pairs of corresponding angles congruent. We have one pair of corresponding angles congruent, the two 55-degree angles. However, the second pair of corresponding angles are not congruent. The third pair of 71 degrees and 70 degrees are also not congruent. It’s not sufficient just to have one pair of corresponding angles congruent to show similarity. And in fact, demonstrating that the other pairs of angles are different and not congruent would demonstrate that these two triangles are definitely not similar. Therefore, the answer to this question is no, these two triangles are not similar.
