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A triangle is a basic polygon used in geometry which consists of three straight lines and three angles. A triangle also possesses three vertices (corners). Commonly, there are three terms used for classifying triangles and this terminology is based on the lengths of a triangle’s sides:

  1. Equilateral Triangle: This type of triangle has 3 equal sides and three angles all of 60 degrees.
  2. Isosceles Triangle: This triangle has 2 sides of equal length and these two sides of the same length also have angles of the same value. These angles are opposite to these two sides.
  3. Scalene Triangle: A scalene triangle has no sides or angles of the same value.

In addition to describing triangles by their sides, they can also be classified by their internal angles:

  1. Right Angled: This triangle has one angle equaling 90 degrees.
  2. Acute Triangle: All angles are less than 90 degrees.
  3. Oblique Triangle: Does not contain a 90 degree angle.
  4. Obtuse Triangle: A triangle in which one of the angles is greater than 90 degrees.

Furthermore, there are two other concepts which are often used in the study of geometry when working with triangles. These terms are known as congruency and similarity. Triangles are described as being congruent when they have the exact same shape and size. These triangles can have all angles and sides being exactly equal, but only three of these six measurements need to be identical when claiming congruency.

Conversely, similar triangles typically have identical angle measurements and proportional sides. However, there are some theorems related to the concept of similarity which have slightly different conditions. 

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