Triangle Sum Theorem
The sum of the measures of the interior angles of a triangle is 180 degrees
The Triangle Sum Theorem states that the sum of the interior angles of a triangle is always equal to 180 degrees. In other words, if you add up the measures of the three angles inside any triangle, the sum will always be 180 degrees.
This theorem holds true for any type of triangle, including scalene, isosceles, and equilateral triangles. It also holds true for both right and obtuse triangles, where one or two of the angles are larger than 90 degrees.
The Triangle Sum Theorem has important applications in geometry, as it allows us to calculate the measure of one angle in a triangle if we know the measures of the other two angles. It also allows us to determine whether a given set of angle measures can form a triangle or not.
For example, if we are given two angle measures in a triangle, we can subtract their sum from 180 to find the measure of the third angle. If the result is between 0 and 180 degrees, then we know that the three angles can form a triangle. If the result is outside of that range, then we know that a triangle cannot be formed with those angle measures.
Overall, the Triangle Sum Theorem is a fundamental concept in geometry, and is essential for solving problems related to triangles and their angles.
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