One of the most fundamental shapes in geometry is a triangle and it has various properties attached to it. There are different forms of triangles and according to their shape, the angles vary. The interior angles that are the angles on the sides should sum up to a perfect 180 degrees. For triangles, you need to study about the inequality theorem according to which, if you pick any 2 sides and add their lengths, then it has to be greater than the length of the third side. This is known as triangle inequality theorem. But you need to understand what the relationship between the sides and angles are. College students are supposed to know how to write a coursework since they might be asked to write on the angles of a triangle and the kind of theorems that apply to it. One side and the largest interior angle of a triangle will always be opposite to each other and this rule applies to one side and the smallest angle as well as the third side and middle-sized angle.
The following section of the article will talk about the differences between interior and exterior angles with the help of holistic explanation of each of the concepts. Once we are done with that, we will then proceed towards the type of triangles and explain each one to you on the basis of the length of the sides and the angles that each side makes with its adjacent sides.
First of all, you need to know the difference between interior and exterior angles. Although the terms are self-explanatory, yet we will go out of our way and explain to you what they mean in detail. Suppose there is a triangle which can be of any size and shape. Understand that the triangle will only have three sides and if not, then it is not a triangle. As for the angles of a triangle, there are three. Since there are three sides in a triangle, each of the vertices makes an angle. Thus, the angles that are present inside the triangle are called interior angles whereas the ones that are outside the triangle are known as exterior angles. But the question arises as to how exactly is an exterior angle formed. The answer is quite simple. You will just have to extend one side of the triangle by a little bit and you will see an angle forming between the new line and the adjacent side of the side that you had extended. This is known as the exterior angle which will vary according to the side that is extended.
So what do we get when we decide to sum all the three angles of a triangle ? The result should be 180 degrees and this is something which remains the same for all forms of triangles. If one side of a triangle has an interior angle of 90 degrees, then the other two sides should sum up to 90 so that the total sum remains 180 degrees. College students are usually made to write thesis definition explaining the relationship between the sides and the angles of a triangle which happens to be one of the most crucial topics for your thesis in college. There are lots of agencies which provide paper writing service to its customers and they specialize in all forms of write-ups from thesis to even turabian paper and all of them come at different prices according to the popularity and experience of the agency.
A triangle can take any shape depending upon the length of the sides. But ideally, if we are asked about the types of triangles, then there are basically three of them.
Firstly, let us focus on an isosceles triangle. Keep this in mind that two sides of an isosceles triangle will always be of the same length and they will form the same angle with the third side. Thus, two angles of an isosceles triangle will have the same value. Next up, we have the equilateral triangle where all the three sides are equal to each other, which points to the fact that the angles of a triangle will also be the same only. Hence, each of the interior angles of an equilateral triangle will measure to 60 degrees. Finally, we have scalene triangle where each of the sides are different from each other which goes on to say that the three interior angles of a triangle will be different from each other.
These are the three types of triangles that exist and all the problems related to triangles will be based on these three types. There are lots of theorems that are based on the triangles and as you go deeper into the concept, you will gradually come across certain theorems which will improve your understanding of the topic altogether. Triangles is considered as one of the most fascinating topics in geometry owing to its theorems and there are lots of thesis topics which can be generated related to triangles. Your approach towards problems related to triangles should be holistic and well researched since there are lots of factors to keep in mind. You might be asked to prove theorems and the reason that you give has to be justifiable enough to ensure that the reviewer gets the crux of the concept. There is still a lot of research being done related to the angles in a triangle as there is a lot of scope. You need to understand the relationship between different types of triangles with their sides and angles. Especially if you are in college and your major happens to be mathematics, then you might have to do a lot of research while drafting an essay on a topic related to triangles.
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We know that interior angles are the ones that are present inside the triangle and the sum of all interior angles is 180 degrees. Thus, at a given point in time, only one of the angles can be more than 90 degrees as the other two angles have to add up to the remaining value. There is the concept of incenter which we have not discussed yet. Let us say we draw a line from all the three vertices of a triangle to their respective opposite sides. The point at which they will meet and bisect is called as an incenter. Now, if you draw a circle which touches all the three sides of the triangle, then the center of the circle will be the same point as the incenter.
One more point to note is that the interior angles will only add up to 180 degrees if the triangle is planar. For those who do not know what planar means, it is any shape that rests on a flat place. Let us say there is a triangle which is lying on a surface that is curved. In this case, the angles might not add up to 180 degrees. As for exterior angles, if we extend one side of a triangle, then it will result in an exterior angle. If we consider the angles of a triangle, then we will notice that the value of the exterior angle will be calculated when the two interior angles are added to each other.