Classifying Triangles by Their Sides
Free printable worksheets on classifying triangles by their sides: scalene, isosceles and equilateral. With an answer key.
Each question gives three side lengths and asks whether the triangle is scalene, isosceles or equilateral. Three different sides is scalene, exactly two the same is isosceles, and all three the same is equilateral.
Every triple on the sheet is a triangle that actually closes. A shape with sides of 2 cm, 2 cm and 9 cm cannot be built — the two short sides never meet — and asking a student to classify it would be wrong rather than merely hard, so the generator does not produce one.
What this worksheet covers
- Classify a triangle as scalene, isosceles or equilateral
- Compare the side lengths to decide
Frequently asked questions
Is an equilateral triangle also isosceles?
By most definitions yes, since isosceles means at least two equal sides. These sheets ask for the most specific name, so a triangle with three equal sides is marked equilateral, never isosceles.
What makes a triangle scalene?
All three sides are different lengths. Sides of 13 cm, 19 cm and 12 cm make a scalene triangle.
Why do the sides never make an impossible triangle?
Because of the triangle inequality: the two shorter sides added together have to be longer than the longest one. Every question here satisfies it, so every shape described can really be drawn.
Does this classify triangles by angles too?
Not on this sheet — it classifies by sides. Acute, right and obtuse angles are covered on the geometry worksheets, which ask about an angle’s measure directly.