Maths
What are the different types of triangles?
Quick answer
Triangles are named by their sides (equilateral, isosceles, scalene) or by their angles (acute, right-angled, obtuse). The three angles of any triangle add up to 180 degrees.
In one sentence
Triangles can be sorted by how many sides are equal, or by the size of their biggest angle, and the three angles always add up to 180 degrees.
Explained
A triangle has three straight sides and three angles. We can name it in two ways.
By its sides:
- Equilateral: all three sides are equal, and all three angles are 60 degrees.
- Isosceles: two sides are equal, and the two angles opposite them are equal too.
- Scalene: no sides are equal, and no angles are equal.
By its angles:
- Acute-angled: all three angles are smaller than 90 degrees.
- Right-angled: one angle is exactly 90 degrees.
- Obtuse-angled: one angle is bigger than 90 degrees.
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You can combine the two ways. A right-angled isosceles triangle, for example, is what you get when you cut a square in half along its diagonal. A triangle cannot have two right angles or two obtuse angles, because its angles would add up to more than 180 degrees.
Here is a handy fact: the three angles in every triangle add up to 180 degrees. If you know two, you can find the third. For 50 and 60 degrees, the third is 180 − 50 − 60 = 70 degrees. Triangles are one family of 2D shapes, and they are strong, which is why engineers use them in bridges and cranes.
Examples
| Triangle | Sides | Angles |
|---|---|---|
| Equilateral | all three equal | 60°, 60°, 60° |
| Isosceles | two equal | 70°, 70°, 40° (acute) |
| Scalene | none equal | 50°, 60°, 70° (acute) |
| Right-angled scalene | 3 cm, 4 cm, 5 cm | 37°, 53°, 90° (about) |
| Obtuse isosceles | two equal | 30°, 30°, 120° |
Common mistakes
- Judging by a drawing. Diagrams are not always to scale. Use the marks that show equal sides or the angle sizes given.
- Mixing up the two systems. "Isosceles" is about sides, "obtuse" is about angles, so one triangle can be both.
- Forgetting 180 degrees. If your three angles add up to something else, check your measuring.
Some books treat an equilateral triangle as a special kind of isosceles triangle. In primary school, they are usually kept as separate groups.
Quick quiz
Types of triangles
Check what you know with 4 quick questions.
Question 1 of 4
Which triangle has all three sides the same length?
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Related topics
2D shapes
2D shapes are flat shapes with length and width but no thickness, like circles, triangles, squares and hexagons. You can draw them on paper.
Angles
An angle measures the amount of turn between two lines that meet at a point. Angles are measured in degrees (°); a right angle is 90° and a full turn is 360°.
Polygons
A polygon is a flat shape made only of straight sides that close up completely. Triangles, squares, pentagons and hexagons are polygons; a circle is not.
Quadrilaterals
A quadrilateral is any flat shape with four straight sides. Squares, rectangles, rhombuses, parallelograms, trapezia and kites are all quadrilaterals, and their angles add up to 360 degrees.
Area of a triangle
The area of a triangle is half of its base times its perpendicular height: A = ½ × b × h. A triangle with base 8 cm and height 5 cm has an area of 20 square centimetres.
Area
Area is the amount of flat space inside a shape, measured in square units like cm² or m². A rectangle 4 cm by 3 cm has an area of 4 × 3 = 12 cm².