 This video is called Relationships of Angles and Sides in a Triangle. What we're going to do is determine the relationship between the measures of the given angles in a triangle. It's really kind of nice because when you have any kind of triangle, should let me draw one a little bit different than that, how about something like this, you look here and you can see that in a triangle, the opposite side of the largest triangle is the longest side, which makes sense. If you find the angle that is the biggest that has the widest opening opposite it, the side opposite or across from it is going to be the longest side because the angle opens up the biggest. So for the same way in a triangle, the opposite side of the smallest angle would be the shortest. So in your picture, if you look for the smallest angle right here, since the smallest angle is the smallest opening, the side and across from it will be the smallest. So that by process of elimination gives you kind of the middle angle or the medium angle will open up to be the medium or mid-length side. So just try some questions using this information. So here I have triangle I, G, H, and we want to name the longest side. I know that my triangle, all the angles have to add up to be in 180 degrees. So if I do 90 plus 24, I have 114. And then if I do 180 minus 114, that gives me 66. So I know that this angle I right here is 66. So to name the longest side, I look at the angles. 90 is my biggest angle, so that will give me my longest side. 24 is my shortest angle, so the side opposite that will give me my shortest side. And 66 is my medium or middle angle, so that will give me my medium side. So the answer to this problem to name the longest side will be side I, H, or H, I, it doesn't matter what order you put the letters in. The next problem, problem number two, gives us a triangle J, K, L. It says to name the smallest angle. Well, this is interesting because they don't give us any information about the angles. They give us side lengths of 5, 6, and 8. Well, let's remember the shortest side, which is my 5, the angle opposite will be my shortest angle. 8, which is my longest side, the angle opposite that will be my long, or not my longest angle, but it would be my largest or my biggest angle. And then 6, well that is the side length that's in the middle, so the angle opposite that will be the one that is in between or in the middle. So to name the smallest angle, it looks like it will be angle L. My next example, I have triangle ABC. They give me side lengths of 50, 54, and 58. Looks like we're going to do some inequalities looking at greater than, less than, or equal to. We're going to compare the angles. So before I actually get into problems three and four, let's spend a little bit of time in our picture. So it looks like 58 is my longest side. So angle B opposite that will be my largest or my biggest angle. 50 side AB is my shortest side, so the angle opposite that will be my shortest or smallest angle. And then since 54 is the side length in the middle, the angle opposite that, angle A will be my side length, or will be my angle that's in the middle or between. So now let's look at this. For problem three, they want us to compare angle B with angle C. Well angle B, I have marked as the largest or the longest or the biggest angle. It wouldn't be the longest, it would be the largest. And angle C is as the smallest one. So when I put in my inequality, remember the alligator always wants, is I was hungry, wants to eat the biggest. So it looks like we're going to eat angle B. So we'll have measure of angle B is greater than the measure of angle C. Now let's look at problem four, A and C. A is marked with an M as my medium or my middle one, and C is marked with an S as my smallest one. So again, the alligator wants to eat what's the biggest. So the sign or the mouth will open up to angle A. This will read measure of angle A is greater than the measure of angle C. Let's try one more. This is similar to the last one where we're doing greater than, less than or equal. But this time we're trying to compare side lengths. When you look at the picture of triangle D, E, F, they only give us information about angle measures. No problem. Let's go ahead. The biggest angle measure looks to be angle D with 67 degrees. So the side opposite that will be our longest. My shortest angle E is 52 degrees. So the side or segment opposite that. The side opposite that will be my shortest. And then 61 is the angle in the middle. It's the middle one. So the side opposite that will be a medium length or in the middle. So let's do some comparing. E, F, I have marked with my largest. And F, D is marked as my smallest. Alligator wants to eat what's biggest. So it's going to eat E, F. So E, F is greater than F, D. And D, E, for problem number six. D, E is marked as a medium or a middle. And E, F is marked as my largest. Alligator wants the teeth opening. Eating what is the biggest. So it looks like we'll have a less than sign in there. So we'll have D, E is less than E, F. Remember when doing problems like this, please notice in the last few problems I totally ignored this stuff. I totally ignored what it was asking me to actually do. And I spent some time up here in my picture filling out what I could. Because once I fill out everything in my picture, it made answering the problems down here very simple and very fast. Always copy down your diagrams, fill in everything that you can. Then go ahead and answer the questions. Good luck.