Properties of Quadrilaterals (Parallelogram, Rhombus, Rectangle, Square, Kite, Trapezium)

Properties of Quadrilaterals
(Parallelogram, Rhombus, Rectangle, Square, Kite, Trapezium)

Some commonly used quadrilaterals with their properties

Properties of Parallelogram

1. Opposite sides are parallel.
2. Opposite sides are equal in length.
3. Opposite angles are equal.
4. Interior angles of same side (consecutive angles) are supplementary (sum is 180 degree).
5. Each diagonal separates the parallelogram into two congruent triangles.
6. Both diagonal of parallelogram divides it into pair of congruent triangles.
7. The diagonals bisect each other.
8. Area of parallelogram is (base)x(height).
9. 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}.
10. Area of parallelogram is (pqsinA)/2. {Here p and q are the length of the diagonals and A is the angle between these diagonals}.
11. Perimeter of parallelogram is 2(sum of two adjacent sides).

Properties of Rhombus

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

Properties of Rectangle

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

Properties of Square

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

Properties of Kite

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

Properties of Trapezium

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