Identify Triangles by Sides

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Identify a triangle by its sides

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

1) Look at the side lengths

A triangle can be:

Equilateral: all 3 sides are equal.
Isosceles: exactly 2 sides are equal.
Scalene: all 3 sides are different.

2) Compare carefully

Write the three lengths in a simple order and check which ones match. If two sides are the same, the triangle is isosceles even if the third side is different. If all three match, it is equilateral. If no sides match, it is scalene.

3) Use the given exact values

If the side lengths involve fractions, radicals, or expressions, simplify them first if needed, then compare the results. Two sides count as equal only when their simplified forms are exactly the same.

4) Check your classification

Make sure your label matches the side comparison:

3 equal sides → equilateral
2 equal sides → isosceles
0 equal sides → scalene

A quick final check is to reread the side lengths one by one and verify that your answer uses only the side information, not the angles.