Concept 3 of 9
Triangles by Sides
Today's big idea
Count the equal sides: 3 is equilateral, 2 is isosceles, 0 is scalene.
Equilateral = 60° each. Right-isosceles = 90° + 45° + 45°.
How it works
👀 What's going on?
Cut a sandwich corner to corner and you get a triangle. Every triangle has three sides, but those sides can all match, partly match, or all differ. That single count decides the name.
💡 Here's the trick
Look at the diagram above. A triangle with all three sides equal is equilateral. One with exactly two equal sides is isosceles, and the angles facing those two sides also match. One with three different sides is scalene. In every triangle the three angles add to 180°.
🪄 How to do it
- 1.Read the three side lengths from the diagram above.
- 2.Count how many of them are equal: three, two or none.
- 3.Three means equilateral, two means isosceles, none means scalene.
✍️ Try it
A triangle has sides 9 cm, 4 cm and 9 cm. What is its name? Then: another triangle has sides 3 cm, 5 cm and 7 cm. What is its name?
The first has two sides of 9 cm, so it is isosceles. The second has three different lengths, so it is scalene.
⚠️ Watch out
You might be thinking that a triangle with three equal sides could also be called isosceles. In this chapter we use the strict names, so isosceles means exactly two equal sides. A triangle of 6 cm, 6 cm and 6 cm is equilateral and nothing else.
🌟 Why this matters
Roof frames, bridges and bicycles are built from triangles because a triangle cannot be squashed out of shape. A builder picks equal sides when both slopes must carry the same load. The name also tells you at once which angles have to match.
Exam tip: Write the three side lengths in order first, and equal pairs then jump out.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“A triangle has sides 6 cm, 6 cm, 10 cm. What TYPE by sides?”
- 1
Count equal sides
Sides 6 and 6 match → 2 equal. 🔺
- 2
Apply the rule
3 equal = equilateral · 2 equal = isosceles · 0 equal = scalene.
- 3
Pick the type
isosceles
- 4
Answer ✓
The triangle is isosceles.
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Count equal sides: 3 = equilateral, 2 = isosceles, 0 = scalene.
TRIANGLE SORT · ROUND 1 OF 2 · SORT ALL 6
Quick check
✅ VERIFICATION
An isosceles triangle has exactly two equal sides. What else must always be true of it?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Triangles by Angles
Acute · Right · Obtuse.