Classifying triangles
A triangle is the simplest closed shape with straight sides — three sides, three corners. Yet there are many kinds of triangle, and every one of them gets two names at once: one for its sides and one for its angles.
By their sides
| Name | Sides |
|---|---|
| equilateral | all three sides are the same length |
| isosceles | exactly two sides are the same length |
| scalene | all three sides are different lengths |
An equilateral triangle is the "perfect" triangle — all three sides equal and all three angles equal (each one is 60°).
To test whether two sides are equal, we either measure with a ruler or look for little tick marks drawn on the sides of the figure. Sides with the same number of ticks are the same length.
By their angles
| Name | Angles |
|---|---|
| acute triangle | all three angles are acute (smaller than a right angle) |
| right triangle | one angle is a right angle |
| obtuse triangle | one angle is obtuse (bigger than a right angle) |
A triangle has only one right or obtuse angle at most — never two of them. Otherwise the three angles would not add up properly.
Both names together
Each triangle gets one name from the "sides" table and one from the "angles" table. Examples:
- An equilateral triangle is always an acute triangle too (all angles 60°).
- A right isosceles triangle has one right angle and two equal sides — like the triangle you get when you cut a square along the diagonal.
- A scalene obtuse triangle has all three sides different and one big angle. The roof of a tilted house often has this shape.
A useful fact
The three angles inside a triangle always add up to 180° (a straight angle, half a turn). You don't need to prove this in Year 4, but it is worth remembering — it tells us why a triangle can never have two right angles: 90 + 90 = 180, with nothing left for the third angle.
A worked example
A triangle has sides of length 5 cm, 5 cm and 7 cm, and one obtuse angle. Name it.
- Two sides equal → isosceles.
- One obtuse angle → obtuse triangle.
Full name: an obtuse isosceles triangle.
Another triangle has angles 60°, 60° and 60°. What is it?
- All three angles equal → all three sides equal too → equilateral.
- All angles smaller than 90° → acute.
Full name: an equilateral (acute) triangle.