Introduction for angle sum property of quadrilateral

Introduction for angle sum property of quadrilateral:

              A quadrilateral is a two-dimensional figure created by connecting four segments endpoint to endpoint with each segment intersecting exactly two others. It also has four sides and four angles. Sum of interior angle of any polygon is (n-2) 180^o. Here quadrilateral has four sides so interior angle is (4-2)180^o = 360^o.Exterior angle of any polygon is 360^o so the exterior angle of a quadrilateral is 360^o.

Types of Quadrilaterals

• Trapezoid
• Parallelogram
• Square
• Rectangle
• Rhombus 

 

Angle Sum Property of Quadrilateral- Trapezoid

• The sum of the adjacent angles are equal to 180^o
• The sum of all the interior angles are equal to 360^o 

• In the above figure  the sum of two adjacent angles are equal to 180^o
        100 + 80 = 180
        100 + 80 = 180
• The sum of all the internal angles are equal to 360^o
         100 + 100 + 80 + 80 = 360

        

Angle sum property of Parallelogram:

• The opposite angles of a parallelogram are equal
• The opposite sides of a parallelogram are parallel

 

• In the above diagram The sum of all the interior angles are equal to 360^o

               110 + 70 + 110 + 70 = 360

• The sum of the adjacent angles are equal to 180^o
               110 + 70 = 180
            110 + 70 = 180

Angle sum property of Square

• All the four sides of a square are equal
• All the four angles of a square are equal, And the angles are equal to 90^o

• The sum of all the internal angles are equal to 360^o

     

• In the above diagram, All the four angles of a square are equal, And the angles are equal to 90^o
                    90 + 90 + 90 + 90 = 36^o

Angle Sum Property of Quadrilateral- Rectangle

• All the four angles of a square are equal, And the angles are equal to 90^o

• The sum of all the internal angles are equal to 360^o

    

• In the above diagram, The sum of all the internal angles are equal to 360^o
               90 + 90 + 90 + 90 = 360^o

Angle sum property of Rhombus

• The sum of all the internal angles are equal to 360^o

• Opposite angles of a rhombus are equal 

• In the above diagram, The sum of all the internal angles are equal to 360^o
                     115 + 65 + 115 + 65 = 360