Triangle Angle Sum Theorem
The sum of the measures of the angles of a triangle is 180.
The Triangle Angle Sum Theorem states that the sum of the interior angles of a triangle is always equal to 180 degrees. This means that no matter what type of triangle you are dealing with, whether it is scalene, isosceles, equilateral or right-angled, the sum of the angles inside the triangle will always be equal to 180 degrees.
The easiest way to understand this theorem is to visualize it with an example. For instance, let’s take a look at an equilateral triangle, which has all three sides and angles equal. Each angle in an equilateral triangle measures 60 degrees. Therefore, the sum of all three angles will be 60+60+60= 180 degrees. Alternatively, we could also consider a scalene triangle, in which all three angles are unequal. In such a case, when the measure of the three angles are added together, the total sum will still be 180 degrees.
This theorem is useful in a number of ways. It can be used to prove other geometric theorems, such as the exterior angle theorem. It is also useful in practical applications, such as in architecture, where it is important to have precise measurements and angles to ensure that structures are stable and secure.
In summary, the triangle angle sum theorem states that the sum of the interior angles of a triangle is always equal to 180 degrees, and this holds true for all types of triangles.
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