Before we discuss the Quadrilateral Theorem, let us discuss what is Quadrilateral in Mathematics. A quadrilateral is a polygon with four vertices, four enclosed sides, and 4 angles. The sum of the interior angles of each polygon is 360-degrees and the sum of exterior angles should be 180-degrees.
The length and angles could be different and named as per the dimensions like a parallelogram, rectangle, squares etc. Each of the polygons has different properties based on the sides and its angles. Now let us have a quick look at angle sum property or Quadrilateral theorem now.
In the figure given above, ABCD is the quadrilateral and ABC, BCD, and CDA, DBA are the internal angles, AC is the diagonal that divides the quadrilateral into two triangles further. These are the triangle ABC and triangle ADC. As we know that sum of interior angle should be 360-degrees, so, based on the quadrilateral theorem, the sum of ABC + BCD + CDA + DBA would be 360-degrees.
A parallelogram is a special case of Quadrilateral having four sides whose opposite sides are equal and parallel. It means that the parallelogram has a definite pair of opposite sides that are equal in length and parallel too. However, two pairs can of different lengths from each other. Visually, parallelogram looks very much similar to leaning rectangle because rectangle was busy throughout the day and now it is leaning up against the wall. There are two coherent properties for the parallelogram Quadrilateral as given below-
Now you understood the basic Quadrilateral Theorem, what is quadrilateral and its properties too. With the help of quadrilateral Theorem formula, you could solve typical problems in the real life. A quadrilateral may be Trapezium as well or it could be a Rhombus. Here, the side and angle properties would be different and they are dedicated to special theorems too.
Another way to classify the types of quadrilaterals is as given below –