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​What is a triangle? In addition to having three sides and three angles,there are four basic rules or theorems that a shape must satisfy in order to be classified as a triangle.


Theorem 1. This theorem states that when adding the side lengths of a triangle, the sum of two sides of a triangle must be greater than the length of the third side.

Types of Triangles

3x6x4 Triangle
3
4
6
6 + 3 > the third side 4
4+3 > the third side 6
6+4 > the third side 3
Interior angles = 180
60 + 60 +60  = 180 degrees
Measure exterior angle triangle
​30°
150°
Interior and Exterior angles are supplementary
equilateral triangle
Theorem 2. The sum of the interior angles of a triangle equal 180 degrees.
​Theorem 3. The measure of an exterior angle is formed by extending one of the sides. Furthermore, the interior and exterior angles created, are supplementary.

Theorem 4.Proportionality of Triangles. The longest side of a triangle is opposite the largest angle, and the shortest side is opposite the smallest angle.

a line
a line
a line
a line
triangle with 50 30 110 degree angles
​Longest Side
​Shortest Side
a line
​Triangles can be classified by the length of their sides.

Scalene triangle

Three different side lengths

Three different angle measures

Isosceles triangle

At least two congruent sides

At least two congruent angles

Equilateral triangle

Three congruent sides

Three congruent angles The angle measure equals 60 degrees

Triangles can also be classified by their angles.

There are three angles often associated with triangles
  • Acute angles are less than 90 degrees
  • Right angles are exactly 90 degrees
  • Obtuse are greater than 90 degrees

All triangles have two acute angles and the third angle determines the type of
Triangle you have.

Acute triangle

Triangle with three angles that measure less than 90 degrees

Obtuse triangle

Triangle with one angle greater than 90 degrees

Right triangle

Triangle with one right angle ( 90 degrees)

The other two angles are complementary