Triangles

In short: The three angles in any triangle add to $180^{\circ }$. An equilateral triangle has 3 equal sides and three $60^{\circ }$ angles, an isosceles triangle has 2 equal sides and 2 equal angles, and a scalene triangle has no equal sides.

Before you start

• A straight line is $180^{\circ }$ and a right angle is $90^{\circ }$ (see Types of Angles).
• Acute, right and obtuse angles.
• Equal sides in a diagram are shown with matching little dashes called tick marks.

Angle sum of a triangle

Naming triangles by their sides

Naming triangles by their angles

• Acute-angled: all three angles are acute.
• Right-angled: one angle is $90^{\circ }$. The other two add to $90^{\circ }$. The longest side, opposite the right angle, is called the hypotenuse.
• Obtuse-angled: one angle is obtuse.

A triangle can only have one right angle or one obtuse angle, because the other two must still fit into $180^{\circ }$.

The exterior angle

If you stretch one side of a triangle past a corner, you make an exterior angle outside the triangle.

Why? The exterior angle and the third inside angle make a straight line of $180^{\circ }$, and so do all three inside angles. Take the third angle away from both and you are left with exterior $=a+b$.

Quick summary

• The angles in a triangle add to $180^{\circ }$.
• Equilateral: 3 equal sides and three $60^{\circ }$ angles.
• Isosceles: 2 equal sides and 2 equal base angles.
• Scalene: no equal sides or angles.
• In a right-angled triangle, the other two angles add to $90^{\circ }$. The longest side is the hypotenuse.
• An exterior angle equals the sum of the two opposite interior angles.

Quiz