Explanation:

A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted  ABC.

By relative lengths of sides

Triangles can be classified according to the relative lengths of their sides:

§  In an equilateral triangle all sides have the same length. An equilateral triangle is also a regular polygon with all angles measuring 60°. In an isosceles triangle, two sides are equal in length^. An isosceles triangle also has two angles of the same measure; namely, the angles opposite to the two sides of the same length; this fact is the content of the Isosceles triangle theorem. Some mathematicians define an isosceles triangle to have exactly two equal sides, whereas others define an isosceles triangle as one with at least two equal sides. The latter definition would make all equilateral triangles isosceles triangles. The 45-45-90 Right Triangle, which appears in the Tetrakis square tiling, is isosceles.

§  In a scalene triangle, all sides are unequal. The three angles are also all different in measure. Some (but not all) scalene triangles are also right triangles.

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http://en.wikipedia.org/wiki/Triangle

Right triangle

A right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90 degree angle). (Our solved example in mathguru.com uses this concept)

http://en.wikipedia.org/wiki/Right_triangle

The above explanation is copied from Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported License.

(Our solved example in mathguru.com also uses the below concept. This is our own explanation, it is not taken from Wikipedia.)

The sum of all the angles of a Triangle is 180(Angle Sum Property of a Triangle)