Inequalities

The exterior angle of a triangle is always greater than either of its corresponding interior angles:

Exterior Angle

$$\\ m\angle A> m\angle C\\ m\angle A> m\angle D\\$$

Two important things to remember is that if one side of a triangle is longer than another side (compare BC and AB in the triangle below BC > AB) then the angle opposite of the longer side is always greater than the angle opposite (A > B) of the shorter side. Likewise if one angle is greater than another angle (A > B) then the side opposite of the greater angle is always longer than the side opposite the lesser angle (BC > AB).

triangle

The sum of the lengths of any two sides in a triangle is always greater than the length of the third side:

Triangle

$$AB+BC>AC$$

$$AC+AB>BC$$

$$BC+AC>AB$$

Video lesson

List the sides of the triangle in the order from shortest to longest.