Section 12.3: Triangles

Property

A triangle can be constructed when given sufficient information: three side lengths (SSS), two sides and the included angle (SAS), two angles and the included side (ASA), or two angles and a non-included side (AAS).
The triangle inequality must be satisfied: the sum of any two sides must be greater than the third side.

Examples

Property

For any triangle with side lengths $a$, $b$, and $c$, the sum of any two sides must be greater than the third side:

Examples

Property

Triangles can be classified by the lengths of their sides:

• All three sides of an equilateral triangle are equal in length.
• In an isosceles triangle, two sides are equal in length.
• In a scalene triangle, all three sides have different lengths.

Examples

• A triangle with side lengths of 7 cm, 7 cm, and 7 cm is an equilateral triangle.
• A triangle with side lengths of 5 inches, 5 inches, and 8 inches is an isosceles triangle.
• A triangle with side lengths of 4 m, 6 m, and 9 m is a scalene triangle.

Explanation

A triangle's name can also come from its side lengths. 'Equilateral' means all sides are equal. 'Isosceles' means two sides are equal. 'Scalene' means no sides are equal—they all have different lengths.