Concurrent Quadrilaterals

Quadrilaterals are one of the geometric shapes with four sides. Basically quadrilaterals are the polygon with four sides. Quadrilaterals are of different types. Concurrent means same. Concurrent Quadrilaterals are the quadrilaterals with same sides and similar angles. In this article we shall discuss about the concurrent quadrilaterals. Also we shall discuss about the fascinating properties of the concurrent quadrilaterals

Types of Concurrent Quadrilaterals:

Square:

 

   Basically square is a geometric shape with four concurrent sides. Also the interior angle of a square measures 90° on each side which is concurrent. The diagonals of the square forms four isosceles right triangle.
Rectangle:

 

   Rectangle is a shape with four sides. The opposite sides of a rectangle are concurrent. The angle measures 90° for each side of the rectangle. The diagonals are concurrent for a rectangle.
Rhombus:

 

   Rhombus has the properties similar to square. The opposite angles are similar and all the sides are concurrent.
Parallelogram:

   The parallelogram has the similar properties of a rectangle. Opposite sides of a parallelogram are concurrent. And the opposite angles are similar.

Sample Problems based on Concurrent Quadrilaterals:

Example 1:
What is the measure of the missing angle in the parallelogram?

 

Solution:
   60° + 120° + 120° + x° = 360°
                        300° + x° = 360°
            300° + x° – 300° = 360° - 300°
                              X° = 60°
Example 2:
In a rectangle has ABCD, find the missing angle and missing sides of the rectangle.

Solution:
Missing Angles:
   Each angle of a rectangle will be 90°. So the missing angles of the rectangle are 90° each.
      90° + 90° + 90° + 90° = 360°
Missing Sides:
   We know that the opposite sides of a rectangle are similar.
     So, CD = 10cm
    And AD = 4cm
Example 3: 
Determine the missing values from the given parallelogram and explain the reason.

Solution:

   A = 110°  (Opposite angles of a parallelogram are equivalent)
   B = 70°    (Opposite angles of a parallelogram are equivalent)