scalene triangle
a triangle with no congruent sides
A scalene triangle is a type of triangle where all three sides are unequal in length. In other words, no two sides in a scalene triangle are the same length. This is in contrast to an isosceles triangle, where two sides are equal in length.
Scalene triangles have a unique set of properties due to their unequal sides. For example:
1. All interior angles are also unequal. This means that the measures of the angles in a scalene triangle will all be different.
2. Scalene triangles do not have any lines of symmetry. In other words, there is no way to divide a scalene triangle into two congruent parts.
3. The area of a scalene triangle can be calculated using Heron’s formula, which takes into account the lengths of all three sides.
4. As there are no congruent sides, to solve for the unknown parts of a scalene triangle, one usually needs to use trigonometric functions such as sine, cosine, and tangent.
It is also interesting to note that any non-degenerate triangle (i.e. a triangle that has positive area) can be transformed into a scalene triangle through a series of rigid transformations such as translations, rotations, and reflections.
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