## Properties of Quadrilaterals

(Parallelogram, Rhombus, Rectangle, Square, Kite, Trapezium)

## Some commonly used quadrilaterals with their properties

## Properties of Parallelogram

- Opposite sides are parallel.
- Opposite sides are equal in length.
- Opposite angles are equal.
- Interior angles of same side (consecutive angles) are supplementary (sum is 180 degree).
- Each diagonal separates the parallelogram into two congruent triangles.
- Both diagonal of parallelogram divides it into pair of congruent triangles.
- The diagonals bisect each other.
- Area of parallelogram is (base)x(height).
- Area of parallelogram is (abSinK). {Here a and b are the length of two adjacent sides and K is the angle between these two sides}.
- Area of parallelogram is (pqsinA)/2. {Here p and q are the length of the diagonals and A is the angle between these diagonals}.
- Perimeter of parallelogram is 2(sum of two adjacent sides).

## Properties of Rhombus

- Opposite sides are parallel.
- All sides are equal in length.
- Opposite angles are equal.
- Interior angles of same side (consecutive angles) are supplementary (sum is 180 degree).
- Each diagonal separates the rhombus into two congruent triangles.
- Both diagonal of rhombus divides it into four congruent triangles.
- The diagonals bisect each other at 90 degree.
- Area of rhombus is (base)x(height).
- Area of rhombus is (a²)SinA. {Here a is the length of sides and A is the angle between the two sides}.
- Area of rhombus is (pq)/2. {Here p and q are the length of the diagonals}.
- Perimeter of rhombus is 4(length of a side).

## Properties of Rectangle

- Opposite sides are parallel & adjacent sides are perpendicular.
- Opposite sides are equal in length.
- All interior angles are of 90 degree.
- Interior angles of same side (consecutive angles) are supplementary (sum is 180 degree).
- Each diagonal separates the rectangle into two congruent triangles.
- Both diagonals of rectangle divides it into pair of congruent triangles.
- The diagonals bisect each other.
- Area of rectangle is equal to the product of the two adjacent sides.
- Perimeter of rectangle is 2(sum of two adjacent sides).

## Properties of Square

- Opposite sides are parallel & adjacent sides are perpendicular.
- All sides are equal in length.
- All interior angles are of 90 degree.
- Interior angles of same side (consecutive angles) are supplementary (sum is 180 degree).
- Each diagonal separates the square into two congruent triangles.
- Both diagonal of square divides it into four congruent triangles.
- The diagonals bisect each other at 90 degree.
- Area of square is (a²). {Here a is the length of sides of the square}.
- Perimeter of square is 4(length of a side).

## Properties of Kite

- It has two pair of adjacent equal sides.
- It has a pair of equal opposite angles (obtuse angle).
- Two diagonals intersect at 90 degree.
- Longer diagonal bisects the shorter diagonal at 90 degree.
- The longer diagonal divides the kite into two congruent triangles.
- The shorter diagonal divides the kite into two isoscales triangle.
- The longer diagonal bisects the pair of opposite angles.
- Area of the kite if (pq/2) {Here p and q are the length of the diagonals}.
- Perimeter of the kite is 2(sum of non equal adjacent sides).

## Properties of Trapezium

- One pair of opposite sides are parallel.
- Area of trapezium is (1/2)(sum of parallel sides)(hieght).
- Perimeter of the trapezium is equal to the sum of all sides.