Types of Triangles: Properties Guide

G2Triangles

Four families of triangle.

Triangles are classified by their sides and their angles.

The triangle family.

Equilateral

3 equal sides · all 60°

Isosceles

2 equal sides

Scalene

all sides different

Right-angled

one 90° angle

Every triangle's angles add up to 180° — whatever its type.

Learn the Types

1Check the sides.

Equilateral: 3 equal. Isosceles: 2 equal. Scalene: all different.

3 · 2 · 0 equal

2Check the angles.

Equilateral: all 60°. Isosceles: 2 equal base angles. Right-angled: one angle is exactly 90°.

60° · 60° · 60°

3A triangle can be two types.

A right-angled triangle can also be isosceles (45°, 45°, 90°).

45-45-90

💡 Key IdeaEqual sides sit opposite equal angles — 2 equal sides means 2 equal angles, always.

Worked Example

Classify each triangle.

Sides 7 cm, 7 cm, 7 cm

equilateral

Angles 30°, 60°, 90°

right-angled scalene

Sides 5 cm, 5 cm, 8 cm

isosceles

Watch Out! Common Mistakes

Calling every triangle with a square corner ‘just right-angled’.

Look twice! 45°, 45°, 90° is right-angled AND isosceles — a triangle can belong to two families.

Isosceles with equal angles in the wrong place.

Wrong! The two equal angles sit opposite the two equal sides — at the base of the matching sides.

An equilateral triangle with a 90° angle.

Impossible!

Equilateral means all angles are 60° (they must be equal and total 180°). No equilateral triangle has a right angle.

⬇ Cheat Sheet

TRIANGLES

Equilateral: 3 equal sides, all angles 60°.
Isosceles: 2 equal sides, 2 equal angles.
Scalene: all sides and angles different.
Right-angled: one 90° angle (can also be isosceles or scalene).

Example: 5, 5, 8 cm → isosceles · 30°, 60°, 90° → right-angled scalene

📄 Free printable: Download the Triangles cheat sheet (PDF) — keep it by your child's desk.

Quick summary

Equilateral: three equal sides, three 60° angles.
Isosceles: two equal sides and two equal angles opposite them.
Scalene: no equal sides or angles.
Right-angled: one 90° angle — and it can be isosceles or scalene too.

Frequently asked questions

What are the four types of triangle?

Equilateral (3 equal sides), isosceles (2 equal), scalene (none equal) and right-angled (one 90° angle). The first three describe sides; right-angled describes an angle, so types can combine.

Can a triangle be right-angled and isosceles?

Yes — the 45°, 45°, 90° triangle has two equal sides and a right angle.

Why can't an equilateral triangle have a right angle?

Its three equal angles must total 180°, so each is exactly 60°.

Triangles