# Write an inequality relating the given side lengths right

We know that 6 plus x is going to be equal to Let's say this side has length 6. We have been given that? Then we keep making that angle smaller and smaller and smaller all the way until we get a degenerate triangle.

If you subtract 6 from both sides right over here, you get 4 is less than x, or x is greater than 4. For this theorem, we only have two inequalities since we are just comparing an exterior angle to the two remote interior angles of a triangle. P, and then? Thus, we know that the measure of? This inequality has shown us that the value of x can be no more than Wyzant Resources features blogs, videos, lessons, and more about geometry and over other subjects. The Triangle Inequality Theorem, which states that the sum of the lengths of two sides of a triangle must be greater than the length of the third side, helps us show that the sum of segments AC and CD is greater than the length of AD. Now, we can work on some exercises to utilize our knowledge of the inequalities and relationships within a triangle. Let's begin our study of the inequalities of a triangle by looking at the Triangle Inequality Theorem. Triangle inequality theorem Video transcript Let's draw ourselves a triangle. This fact allows us to say that? So if you want this to be a real triangle, at x equals 4 you've got these points as close as possible. GO Inequalities and Relationships Within a Triangle A lot of information can be derived from even the simplest characteristics of triangles. We have been given that? A, is has the largest measure in?

So we're trying to maximize the distance between that point and that point. The Triangle Inequality Theorem, which states that the sum of the lengths of two sides of a triangle must be greater than the length of the third side, helps us show that the sum of segments AC and CD is greater than the length of AD.

So the first question is how small can it get? And just using this principle, we could have come up with the same exact conclusion.

KLM and? And what I'm going to think about is how large or how small that value x can be.

## Write an inequality relating the given side lengths right

That any one side of a triangle has to be less, if you don't want a degenerate triangle, than the sum of the other two sides. ACD and? ECB are congruent since they are vertical angles. Let's see if our next inequality helps us narrow down the possible values of x. So, in order from least to greatest angle measure, we have? So let's try to do that. The corresponding side is segment DE, so DE is the shortest side of? Judging by the conclusion we want to arrive at, we will most likely have to utilize the Triangle Inequality Theorem also. So this side is length 6. So now the angle is getting smaller. A, is has the largest measure in? Angle-Side Relationships If one side of a triangle is longer than another side, then the angle opposite the longer side will have a greater degree measure than the angle opposite the shorter side. So we have our 10 side.

And let's say that this side right over here has length x. Well in this situation, x is going to be 6 plus 10 is

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