Types of Triangles

What makes a triangle?

A triangle is one of the simplest shapes in geometry. It is a flat (2D) shape with exactly three straight sides and three corners. Each corner, where two sides meet, is called a vertex (the plural is vertices), and inside each vertex there is an angle.

You can see triangles everywhere once you start looking: in the slice of a pizza, the sail of a boat, a slice of cheese, a road sign warning of danger, and in the strong frames of bridges and roofs. Engineers love triangles because they are very stiff and do not wobble like a square frame can.

There are two different ways to sort triangles into types. We can group them by the length of their sides, or by the size of their angles. Both ways are useful, and a single triangle has a name from each group at the same time.

Sorting triangles by their sides

When we look at how long the sides are, there are three types.

• Equilateral triangle — all three sides are the same length. Because the sides are equal, all three angles are equal too, and each one is exactly 60° (since 60 + 60 + 60 = 180).
• Isosceles triangle — exactly two sides are the same length. The two angles opposite those equal sides are also equal to each other.
• Scalene triangle — no sides are the same length. All three sides are different, and all three angles are different.

A handy trick: equilateral contains the word "lateral", which means side, so it reminds you all the sides are equal.

Sorting triangles by their angles

When we look at the angles inside, there are three more types.

• Acute triangle — all three angles are less than 90° (all the corners look sharp and "pointy").
• Right-angled triangle — has one angle of exactly 90° (a square corner). We usually mark this angle with a small square symbol.
• Obtuse triangle — has one angle that is bigger than 90° (one corner looks wide and "open").

A triangle can only ever have one right angle or one obtuse angle. It can never have two, because the three angles must add up to 180° — and two angles of 90° or more would already use up all 180° on their own. You can read more about acute, right and obtuse angles in our lesson on angles and lines.

A diagram in words

Picture three triangles drawn side by side.

The first is an equilateral triangle: it looks perfectly balanced, like a mountain peak, with all three sides the same length. Each side has a small dash through it to show the sides are equal.

The second is a right-angled triangle: imagine an "L" shape filled in. The bottom side is flat, the left side stands straight up, and a sloping line joins their two top ends. A tiny square is drawn in the bottom-left corner to show that angle is exactly 90°.

The third is an obtuse, scalene triangle: a long, low, leaning shape. All three sides are clearly different lengths, and the corner on the left is stretched wide open — bigger than a square corner.

Worked example 1

A triangle has sides of 5 cm, 5 cm and 8 cm. What type is it (by sides)?

Two of the sides (5 cm and 5 cm) are equal, and one (8 cm) is different. Because exactly two sides match, this is an isosceles triangle.

Worked example 2

A triangle has angles of 40°, 50° and 90°. What type is it (by angles)? And do the angles add up correctly?

First, add the angles: 40 + 50 + 90 = 180°, so the triangle is valid. One angle is exactly 90°, so it is a right-angled triangle.

Worked example 3

A triangle has angles of 30°, 30° and 120°. Describe it in two ways.

The angles add to 30 + 30 + 120 = 180°, so it is valid. One angle (120°) is bigger than 90°, so by its angles it is obtuse. The two 30° angles are equal, which means two sides are equal, so by its sides it is isosceles. We can call it an obtuse isosceles triangle.

Why this matters

Naming triangles is not just a labelling game. The type of triangle tells you about its hidden properties before you even measure it. If you know a triangle is equilateral, you instantly know every angle is 60°. If you know it is isosceles, you know two of its angles are equal, which lets you work out a missing angle. Right-angled triangles are the most important of all in higher maths — they are the foundation of the Pythagorean theorem and trigonometry, which builders, pilots and game designers use every day. Learning to see and name triangle types now gives you a powerful head start.

Activity: triangle hunt and sort

Grab a ruler, a pencil and some paper.

1. Go on a "triangle hunt" around your home or classroom and draw five triangles you find (a coat hanger, a sandwich cut diagonally, a roof shape, a road sign, a slice of pie).
2. For each triangle, measure the three sides with your ruler. Decide whether it is equilateral, isosceles or scalene.
3. Now look at the corners. Decide whether each triangle is acute, right-angled or obtuse.
4. Write a double name for each one, like "right-angled scalene" or "acute equilateral".
5. Challenge: try to draw a triangle that is impossible — for example, a triangle with two right angles. You will discover you cannot, which proves the angles really must add to 180°!