Quadrilaterals

Sum of 4 interior angles = 360 degrees.

The sum of opposite sides of a quadrilateral circumscribed about a circle, is always equal.

Area of quadrilateral = ½ * (one of the diagonals) * (sum of perpendiculars drawn to the diagonal from the opposite vertices).

 

Parallelogram: It has opposite sides parallel to each other and they are equal in dimension. The angles opposite to each other are equal. Two adjacent angles sum up to 180 degrees. The diagonals bisect each other.

The diagonals divide a parallelogram into congruent triangles.

The parallelogram inscribed in a circle is a rectangle.

The parallelogram circumscribed about a circle is a rhombus.

Perimeter of a parallelogram = 2 * (sum of any two adjacent sides).

If the diagonals of a parallelogram are equal, then the parallelogram is a rectangle.

 

O = Point of intersection of diagonals.

Lines joining mid-points of adjacent sides of a parallelogram is a parallelogram.

Rectangle: It is a parallelogram with opposite sides equal. 

Opposite angles are equal to 90 degrees. The diagonals are equal and they bisect each other.

The diagonals in a rectangle inscribed in a circle are equal to the diameter of the circle.

Midpoints of adjacent sides of a rectangle join together to form a rhombus.

Area of a rectangle = length * breadth.

Perimeter of rectangle = 2 * (length + breadth).

Rhombus:

 

Square:

 

 And finally,