Types of triangles

A triangle is the only polygon that cannot be bent out of shape without making a side longer or shorter. That is exactly why it turns up in bridges, roofs and cranes. It is also the simplest polygon, because with only three sides and three corners you can already work out a surprising amount. Here you learn to recognise and sort triangles.

The angle sum is always 180°

In every triangle the three interior angles together make exactly 180°, no matter how the triangle looks. That is the single most important rule. If you know two angles, you find the third at once: with 90° and 40° there remains 180° − 90° − 40° = 50°. This lets you compute missing angles instead of measuring them.

Sorting by sides

By their sides there are three kinds. If all three sides are equally long, the triangle is called equilateral. If exactly two sides are equal, it is isosceles. If all three sides have different lengths, it is called scalene or a general triangle. Some books already call a triangle isosceles when at least two sides are equal, and there the equilateral triangle counts as a special case of it. Here we keep the three kinds neatly apart. In an equilateral triangle, by the way, all angles are equal as well, namely 60° each.

Sorting by angles

By their angles there are likewise three kinds. If a triangle has a right angle of 90°, it is right-angled. If all angles are smaller than 90°, it is acute. If one angle is larger than 90°, it is obtuse. Because the angle sum is 180°, a triangle can only ever have at most one right or obtuse angle.

Angles in an isosceles triangle

In an isosceles triangle the two equally long sides are called the legs, and the third side is the base. Where the legs meet lies the apex. And now the neat property: the two angles at the base, the base angles, are equal. If you know the angle at the apex, you find the other two easily. If the apex is 80°, then 180° − 80° = 100° remain for both base angles together, so 50° each.