Triangle Properties

A triangle is a three-sided polygon. The notation that is generally used is to name their vertices with the capital letters A, B and C (but they can be others, as long as they are capital letters) and sides opposite these vertices are identified with lowercase letters.

A Triangle must meet certain properties to be considered as such. some of them are the following:

  • The sum of the interior angles of a triangle is equal to 180°.
  • Each equilateral triangle is equiangular, that is, the measures of its internal angles are equal, in this case each angle measures 60 °
  • If two sides of a triangle have the same measure, then the opposite angles also have equal measure.
  • In a triangle, a larger side is opposite a larger angle.
  • The value of an exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles.
  • One side of a triangle is smaller than the sum of the other two and larger than their difference. a (b + cab) – c

A triangle widely used in trigonometry is the right triangle, in which the study of the relationship between its sides is made by the Pythagorean theorem.

Pythagorean Theorem: Pythagoras enunciated the famous theorem that bears his name and that relates the sides of a right triangle. This theorem says:

“The area of ​​the square built on the hypotenuse of a right triangle is equal to the sum of the areas of the squares built on the legs.”

Triangles are classified according to two criteria: according to their sides and according to their angles, they can be used together or separately:

1. Classification of triangles according to their sides

  • A triangle is equilateral if it has three equal sides.
  • A triangle is isosceles if it has two of its equal sides.
  • A triangle is scalene if it has three unequal sides.

2. Classification of triangles according to their angles

In this case, we look at the angles to make the classification. Namely:

  • A triangle is acute if all its angles are acute.
  • A triangle is right angled, if it has one of its right angles, that is, 90º.
  • A triangle is obtuse if it has one obtuse angle.