What is Triangle?

A triangle is a three-sided shape whose three inner angles must sum to 180 degrees. The largest angle will be across from the longest side while the smallest angle will be across from the shortest side of the triangle. If and only if two sides of a triangle are equal, the angles opposite them will be equal as well.

Properties of Triangles

  • The sum of three interior angles in any triangle is 180 degrees.
  • The sum of any two sides of a triangle must be greater than the third side of a triangle.
  • The longest side of a triangle is opposite the largest angle of a triangle. Conversely, the smallest side of a triangle is opposite the smallest angle of a triangle.
  • Exterior angle of a triangle is equal to sum of two remote interior angles.

Types of Triangles

A triangle with two equal sides is called isosceles. The angles opposite the equal sides are called the base angles, and they are congruent (equal). A triangle with all three sides equal is called equilateral, and each angle is 60 degrees. A triangle with no equal sides (and therefore no equal angles) is called scalene.


Similar Triangles

Two triangles are similar if:

  • Corresponding angles are of the same measurement.
  • The perimeter of each triangle is in the same ratio as the sides.
  • Corresponding sides are all in the same proportion.

To check similarity of triangles, AAA, SAS or SSS rule can be used.