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← Back to Geometry
1Curved vs Straight Lines2Lines, Rays & Line Segments32D Shapes43D Shapes5Triangle Classification6Symmetry7Compound Perimeter

Concept 5 of 7

Triangle Classification: By Side Length

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Today's big idea

A triangle is named by how many of its sides are equal, not by how it looks.

Comparing all three pairs of sides is what catches an equal pair sitting apart.

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How it works

👀 What's going on?

A road warning sign, a slice of pizza and a wedge of cheese are all triangles. They still look nothing like each other. What tells them apart is how many of their sides are equal.

💡 Here's the trick

Count equal sidesEquilateral3 equalIsosceles2 equalScaleneall differentSides: 5,5,5 · 6,6,4 · 5,6,7

Look at the three triangles above. The first has all 3 sides equal, and that one is called equilateral. The second has exactly 2 sides equal, and that one is isosceles. The third has all 3 sides different, and that one is scalene. Nothing else matters here, not the size and not which way up it sits.

🪄 How to do it

  1. 1.Read the three side lengths on the triangle above.
  2. 2.Compare all three pairs, so you never miss an equal pair that sits apart.
  3. 3.Three equal is equilateral, exactly two equal is isosceles, none equal is scalene.

✍️ Try it

  1. 1.A triangle has sides of 9 cm, 4 cm and 9 cm. What type is it?
  2. 2.A triangle has a perimeter of 20 cm, and two of its sides are 4 cm and 7 cm. What type is it?
  1. 1.The two 9 cm sides are not next to each other in the list, but they still match. Two equal sides means isosceles.
  2. 2.The third side is 20 minus 4 minus 7, which is 9 cm. The sides 4, 7 and 9 are all different, so it is scalene.

⚠️ Watch out

You might be thinking you can stop after checking the first two lengths. Equal sides are easy to miss when they are not written next to each other. On 9, 4, 9 the first two do not match, so stopping there gives the answer scalene, which is wrong. Compare every pair and the equal sides show up. There is one more thing about names. Some books call a triangle with 3 equal sides isosceles as well, since it does have at least two equal sides. Here the stricter rule is used, so 3 equal sides is always called equilateral.

🌟 Why this matters

Roof trusses, bridge braces and step ladders are all triangles, and the builder picks the type by which sides need to be equal. An equilateral frame shares the load evenly, while a scalene one leans. Naming the type is how you say which job a triangle is doing.
Exam tip: SOF and SilverZone Class 3 questions often give a perimeter and two sides, then ask for the type.

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Watch me solve one

Quanta solves it

“Watch how I think through one of these — then you try.”

THE PROBLEM

“A triangle has sides 8 cm, 8 cm, 5 cm. What type is it?”

  1. 1

    Count equal sides

    Two sides = 8 cm, one side = 5 cm → exactly 2 equal.

  2. 2

    Match to the type

    2 equal → ISOSCELES. (3 equal = equilateral. 0 equal = scalene.)

  3. 3

    Answer ✓

    = Isosceles

Now you try one — same steps, different story 👇

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See it in action

⚡ Time to play!

Tap each side to measure it. Then name the triangle by its equal sides.

TRIANGLES · ROUND 1 OF 3

???

Tap all three sides to measure them.

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Quick check

✅ VERIFICATION

Rohan's triangle is scalene. Which set of side lengths could be his?

⚡ Finish the activity above first to answer.

Keep going!

Up next: Symmetry

A line of symmetry folds a shape into two matching halves.

Concept 6 of 7 →