Skill: Classify triangles by side lengths

Explanation and Free Practice Resources

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.

Detailed Explanation: Classify triangles by side lengths

To classify a triangle by its side lengths, compare the lengths of all three sides.

  • Equilateral: all three sides are equal.
  • Isosceles: exactly two sides are equal.
  • Scalene: all three sides are different.

The triangle’s position or shape in a picture does not matter. Use the side measurements.

Example: A triangle has side lengths 6 cm6\text{ cm}, 6 cm6\text{ cm}, and 4 cm4\text{ cm}.

  1. List the side lengths: 66, 66, and 44.
  2. Compare them. Two sides have the same length: 6 cm=6 cm6\text{ cm}=6\text{ cm}.
  3. The third side, 4 cm4\text{ cm}, is different.
  4. Since exactly two sides are equal, the triangle is isosceles.

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Triangle Classification - Sides


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