Triangles: named twice, by sides and by angles

01 Start here

02 The four kinds

03 Working out the third angle

1. Two angles given. The third is 180° minus the other two. Nothing else is needed.
2. Ticks on two sides. The triangle is isosceles, so the two angles opposite those sides are equal — that is a second fact the drawing gave you without writing it down.
3. Ticks on three sides. Equilateral, so every angle is 60° and there is nothing to work out.
4. A small square in a corner. That angle is 90°, so the other two must share the remaining 90°.
5. Check the answer is possible. Three angles, all positive, adding to exactly 180°.

04 Why a triangle is always 180°

05 How to say them

These are words most children have never said out loud, and a word you cannot say is a word you avoid using. Capitals mark the syllable you lean on. Tap the speaker to hear it.

• trianglesayTRY-ang-guhlmore than onetriangles

  Any closed shape with three straight sides. Its three angles always add up to 180°.

• angle ABC, written ∠ABCsayANG-guhl A B C

  The angle at B, the middle letter. The outer letters say which two sides form it, so ∠ABC is the corner where BA meets BC. Papers name angles this way because once a shape is cut in two, a bare “angle B” no longer says which of the pieces is meant.

• equilateralsayee-kwi-LAT-uh-ruhl

  A triangle with all three sides equal, which forces all three angles to be 60°. From Latin for “equal sides”.

• isoscelessayeye-SOSS-uh-leez

  A triangle with at least two sides equal, and the two angles opposite them equal too. The hardest of these words to say, and the one papers use most.

• scalenesaySKAY-leen

  A triangle with no two sides equal, and so no two angles equal either.

• vertexsayVUR-teksmore than onevertices

  A corner — the point where two sides meet. A triangle has three, which is why it is labelled with three letters.

06 What each level is tested on

The same topic, asked differently as it goes up. The percentage is the share of papers at that level in which it appears.

1. P2

   Recognising a triangle on sight, and counting its sides and corners.

   Practise P2 Triangles — 10 questions →
   48% of P2 papers

2. P4

   Naming triangles by their sides, and the first work with a right angle.

   Practise P4 Triangles — 10 questions →
   17% of P4 papers

3. P5

   Angles in a triangle: finding the third from two given, and using the equal angles of an isosceles.

   Practise P5 Triangles — 10 questions →
   70% of P5 papers

4. P6

   Triangles inside composite figures, where the angle sum has to be used more than once.

   Practise P6 Triangles — 10 questions →
   94% of P6 papers

07 Mistakes worth knowing about

Each of these is wrong. Decide why before you open it.

• ✕“An equilateral triangle is not isosceles.”

  It is one. Isosceles asks for at least two equal sides, and three is at least two — the same way a square is still a rectangle. Papers rely on this.

• ✕“A triangle cannot be both right-angled and isosceles.”

  It can, and it is common: 90°, 45°, 45°. One name describes the angles and the other describes the sides, so a triangle carries one of each.

• ✕“The two ticks are on the sides, so the question tells me nothing about the angles.”

  They tell you a great deal. Equal sides force the angles opposite them to be equal, and that second fact is usually what the question is built on.

• ✕“The angles are 100°, 50° and 40°.”

  That is 190°. Three angles have to total exactly 180°, so adding them up at the end catches most arithmetic slips for free.

• ✕“This triangle is bigger, so its angles are bigger.”

  Size has nothing to do with it. Enlarge a triangle and every angle stays exactly as it was — only the sides get longer.