### Video Transcript

Complete the following using less than, equal to, or greater than. If, in the triangle ๐ท๐ธ๐น, ๐ท๐ธ is greater than ๐ธ๐น, then the measure of angle ๐น blank the measure of angle ๐ท.

To help us solve this problem, Iโve actually sketched a triangle just to give us an understanding of our sides and our angles and which side will be opposite which angle.

First of all, we can see that ๐ท๐ธ is opposite angle ๐น. And also side ๐ธ๐น is opposite angle ๐ท. And these are the two sides that weโre interested in because we have this inequality here that tells us that side ๐ท๐ธ is greater than side ๐ธ๐น. But how is this gonna be useful for finding out whether the measure of angle ๐น is greater than, less than, or equal to the measure of angle ๐ท?

Well, actually, what we have is the angleโside relationship or angleโside relationship theorem. And this is actually something that can actually help us see which angle and which side are gonna be greater in size than the other.

And the angleโside relationship tells us that, in a triangle, the side opposite the larger angle is the longer side. So therefore, well, we know that the longer side is ๐ท๐ธ because ๐ท๐ธ is greater than ๐ธ๐น. So therefore, the angle that is opposite ๐ท๐ธ must be greater than the angle that is opposite ๐ธ๐น.

So from this, we can say that the measure of angle ๐น is gonna be greater than the measure of angle ๐ท. And this is the case because side ๐ท๐ธ is opposite angle ๐น and side ๐ท๐ธ is greater than side ๐ธ๐น and side ๐ธ๐น is opposite angle ๐ท.