Properties of Triangles

In a Nutshell

Triangles are classified by their sides (equilateral, isosceles, scalene) and by their angles (acute, right-angled, obtuse). Each type has its own special properties.

Classified by sides

  • Equilateral: all 3 sides are equal, all 3 angles are 60°60°, and there are 3 lines of symmetry.
  • Isosceles: 2 sides are equal, the 2 base angles are equal, and there is 1 line of symmetry.
  • Scalene: no sides are equal, no angles are equal, and there are no lines of symmetry.

Classified by angles

  • Acute-angled: all 3 angles are less than 90°90°.
  • Right-angled: one angle is exactly 90°90°. The side opposite the right angle is called the hypotenuse and is always the longest side.
  • Obtuse-angled: one angle is greater than 90°90°.

A triangle can belong to one group from each list. For example, an isosceles triangle can also be right-angled (with angles 90°,45°,45°90°, 45°, 45°).

Shape property explorer An interactive diagram that shows different shapes and highlights their key properties such as equal sides, parallel sides, and angles.

Select each triangle type to see its shape and key properties. Tick marks show equal sides.

Watch it work

Question: A triangle has sides of 5 cm, 5 cm and 8 cm. Its angles are 51°,51°51°, 51° and 78°78°. Classify it by sides and by angles.

Have a go

Q1. A triangle has all three sides measuring 6 cm. What type of triangle is it? What are its angles?

Q2. A triangle has sides 3 cm, 4 cm and 5 cm. It has a right angle. Classify it.

Q3. How many lines of symmetry does an isosceles triangle have?

Q4. Can an equilateral triangle be right-angled? Explain.

Q5. A triangle has angles 90°,45°90°, 45° and 45°45°. Classify it by sides and angles.