A triangle is classified by comparing the lengths of its three sides: equilateral triangles have three equal sides, isosceles triangles have exactly two equal sides, and scalene triangles have three different side lengths. The classification depends on measured side lengths rather than the triangle’s orientation or apparent shape, establishing a foundation for connecting side relationships with angle relationships and more advanced geometric reasoning; formal proofs involving the triangle inequality are not included.
To classify a triangle by its side lengths, compare the lengths of all three sides.
The triangle’s position or shape in a picture does not matter. Use the side measurements.
Example: A triangle has side lengths , , and .
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