Triangles and Angles:

Triangle:

A polygon with 3 corners/vertices and three sides/edges is called as a triangle. A triangle with 3 vertices A, B and C is represented by ΔABC

The triangles are classified based on their sides and angles. They are:

• Equilateral Triangle: If a triangle has all 3 sides of equal length and all angles measuring 60 degrees, then it is referred to as equilateral triangle.
• Isosceles Triangle: If a triangle has 2 sides and 2 angles equal, then it is referred to as an isosceles triangle.
• Scalene Triangle: If all the 3 sides and 3 angles of a triangle are unequal, then it is referred to as scalene triangle.
• Right angled Triangle: If a triangle has one of its interior angles as 90 degrees, then it is referred to as a right angled triangle. The side opposite to the right angle is referred to as an hypotenuse and the other 2 sides are called the legs or catheti of the triangle.
• Oblique Triangle: A triangle that does not have any angle equal to 90 degrees, is referred to as oblique triangle.
• Acute Triangle: A triangle that has all interior angles measuring below 90 degrees, is referred to as an acute triangle or acute angled triangle.
• Obtuse angled Triangle: A triangle that has all interior angles measuring greater than 90 degrees, is referred to as an obtuse angled triangle.

Fundamental concepts:

Triangles are acquired to be a two-dimensional plane figure. Following are the basic facts provided by Euclid in books about triangles.

• The sum of the interior angles of a triangle always sums up to 180 degrees.
• An exterior angle is an angle that is supplementary to an interior angle. Exterior angle = Sum of the 2 interior angles that are adjacent to it Sum of the 3 exterior angles = 360 degrees
• Sum of the lengths of any 2 sides of a triangle > Length of the third side (Triangle Inequality)
• Two triangles are said to be similar if each angle of a triangle has the same value as the corresponding angles of the second triangle.
• Two triangles are congruent if they have exactly the same size and shape.

Summary:

Thus, in a triangle the 3 sides and 3 angles decide the type of triangle.