Triangles can be sorted two ways, so read which one the question asks. By sides: equilateral has all three sides equal, isosceles has exactly two equal sides, and scalene has no equal sides. Matching tick marks show equal sides. By angles: acute-angled has every angle less than 90°, right-angled has one angle of exactly 90° (shown by a small square), and obtuse-angled has one angle more than 90°. Turning a triangle never changes its type. If only two angles are given, find the third first: the three angles always add to 180°.
Explore this idea with maths tools
Maths you can move
Build 8 + 5
Tap two gold counters to fill the ten-frame.
8 in the frame + 5 waiting. The total stays the same.
Words to know
- isosceles
- a triangle with two equal sides (and two equal angles)
- scalene
- a triangle with no equal sides
- obtuse angle
- an angle more than 90° and less than 180°
Worked examples
Classify a triangle with angles 60°, 60° and 60° by its sides.
- 1.All three angles are equal.
- 2.So all three sides are equal.
= equilateral
A tilted triangle has a small square in one corner. Classify it by its angles.
- 1.The small square marks a 90° angle.
- 2.Turning does not change the type.
= right-angled
Two angles of a triangle are 50° and 80°. Classify the triangle by its sides.
- 1.Third angle: 180 − 50 − 80 = 50°.
- 2.Two angles are equal, so two sides are equal.
= isosceles
For parents
Method: Check the tick marks for sides and the corners for angles; find a missing angle from 180°.
What to say: Is the question about sides or angles? Which marks tell you that?
Common mistakes:
- Classifies from the two angles given without working out the third angle first.
- Mixes the two ways of classifying: gives an angle name when asked about sides, or a side name when asked about angles.
- Only recognises an isosceles triangle when it stands upright on its odd side; a turned one is called scalene.
- Only sees a right angle when it sits at the bottom corner with one side flat; a tilted right angle is missed.
- Swaps the words acute and obtuse.
- Calls any triangle with equal sides 'equilateral', even when only two sides are equal.