Concept 2 of 6
Sorting Triangles by Sides
Today's big idea
Sort a triangle by how many of its sides are equal, using the tick marks.
Same tick count = equal sides. 3 match = equilateral, 2 = isosceles, none = scalene.
How it works
👀 What's going on?
Every triangle has three sides, but those sides need not match each other. How many of them are equal is the first thing that earns a triangle its name.
💡 Here's the trick
Look at the three triangles above. The little tick marks are the trick: sides carrying the same number of ticks are the same length. All three sides matching means equilateral, exactly two matching means isosceles, and no two matching means scalene. You can name a triangle from the marks without measuring a thing.
🪄 How to do it
- 1.Find the tick marks on each side, as the picture above uses them.
- 2.Count how many sides share the same tick count.
- 3.Three equal is equilateral, exactly two is isosceles, and none is scalene.
✍️ Try it
One triangle has sides of 4 cm, 4 cm and 7 cm. Another has 3 cm, 5 cm and 6 cm. Name each of them.
The 4, 4 and 7 triangle has exactly two equal sides, so it is isosceles. The 3, 5 and 6 triangle has no two the same, so it is scalene. Only the count of equal sides matters, never how long they are.
⚠️ Watch out
You might be thinking an equilateral triangle counts as isosceles too, since it certainly owns two equal sides. Most papers treat isosceles as exactly two. When all three match, call it equilateral.
🌟 Why this matters
Roof trusses, bicycle frames and bridge girders are all built from triangles, because a triangle cannot be pushed out of shape. Which triangle you use depends on the side lengths you have to hand.
Exam tip: Tick marks in a figure tell you which sides are equal, so you rarely need to measure anything.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“A triangle has sides 9 cm, 5 cm, and 7 cm. What type?”
- 1
Look at the side lengths
9, 5, 7. Are any equal?
- 2
Count the matches
All three lengths are different — no two match.
- 3
Match the rule
Zero equal sides = scalene.
- 4
Answer ✓
It's scalene
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Look at each triangle's side lengths. Tap the correct label for each one!
Sides: 5cm — 5cm — 5cm
Sides: 4cm — 4cm — 7cm
Sides: 3cm — 5cm — 7cm
Quick check
✅ VERIFICATION
A triangle has sides of 8 cm, 5 cm and 8 cm. What kind is it?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Sorting Triangles by Angles
Acute, right or obtuse, sort by angles.