A scalene triangle is a type of triangle in which all three sides are of different lengths. In addition, all three interior angles in a scalene triangle are also of different measures. This makes the scalene triangle unique in its lack of symmetry and uniformity.
Key Properties of Scalene Triangles
- No sides of equal length: Each side of a scalene triangle has a different length.
- No equal angles: All interior angles are of different measures.
- The angles are directly related to the sides: The largest angle is opposite the longest side, and the smallest angle is opposite the shortest side.
Examples of Scalene Triangles
Example 1: A triangle with side lengths of 4 cm, 5 cm, and 6 cm is a scalene triangle, as no two sides are equal in length.
Example 2: If a triangle has angles measuring 30 degrees, 60 degrees, and 90 degrees, it is a scalene triangle because all three angles are different.
Scalene Triangles in Geometry
Scalene triangles are often used in problems involving triangle inequalities and trigonometry. They represent the most general form of a triangle, with no special properties like equal sides or angles, making them a frequent subject in general triangle studies.
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