Question Video: Using Properties of Congruence between Two Triangles Mathematics • First Year of Preparatory School

Video Transcript

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 52 degrees.