Fundamentals of triangles

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A polygon which has three sides is called a triangle. It is formed by joining three non-collinear points by a straight line. The lines AB, BC, and CA are called the sides of the triangle. The angles formed by these three lines are called the angles of the triangle and they are represented by A, B and C.

 

Basic properties of triangles

  • The sum of the angles of a triangle is 180o. In the figure above∠A + ∠B +∠C = 1800
  • The sum of any two sides of a triangle is greater than the third side of the triangle. In the figure above, AB+BC>CA or BC+CA>AB or CA+AB>BC
  • An angle formed by one side and the extended portion of an adjacent side at the common vertex is called the exterior angle of the triangle. The exterior angle of a triangle is equal to the sum of the interior opposite angles.

 

Classifying triangles

Triangles are primarily classified on the basis of their sides or angles.

On the basis of sides

 

Clockwise from top left, scalene triangle, isosceles triangle and equilateral triangle.

 

Scalene Triangle: A triangle in which all the three sides are unequal is a scalene triangle.

Isosceles triangle: A triangle in which two sides are equal is an isosceles triangle. The angles opposite to the equal sides are also equal.

Equilateral triangle: A triangle in which all the three sides are equal is an equilateral triangle. All the three angles of an equilateral triangle are equal to 600.

Length of altitude = (√3/2)a

Area of an equilateral triangle =(√3/4)a2

 

On the basis of angles

 

Clockwise from top left - acute angle triangle, obtuse angle triangle, right angled triangle

 

Acute angled triangle: A triangle in which all the three angles are acute is an acute angled triangle.

Obtuse angled triangle: A triangle in which one angle is obtuse is an obtuse angled triangle. The side opposite to the obtuse angle is the greatest side of the triangle.

Right angled triangle: A triangle in which one angle is right angle is a right angled triangle. The side opposite to the right angle is called the hypotenuse and is the greatest side of the triangle. In the right triangle ABC below, B is the right angle and AC is the hypotenuse. Here, AC2 = AB2 + BC2. This is called the Pythagoras theorem.

 


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