Quadrilateral: Parallelogram
A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides are parallel and equal in length. The diagonals bisect each other.
Properties of Parallelogram
- Each diagonal divides the quadrilateral into two congruent triangles with the same orientation.
- The opposite sides are parallel and equal in length.
- The diagonals bisect each other.
- The opposite angles are equal in measure.
- The sum of the squares of the sides equals the sum of the squares of the diagonals. (Parallelogram Law)
- Adjacent angles are supplementary (180 degrees).
- Square, Rectangle and Rhombus are special types of parallelograms.
Perimeter & Area of Parallelogram
The perimeter of parallelogram is sum of the length of its sides. Perimeter = 2(L + B)
Area of parallelogram is multiplication of its longer side and distance between them. Area = L * H
Parallelogram Law
It states that the sum of the squares of the lengths of the four sides of a parallelogram equals the sum of the squares of the lengths of the two diagonals. If ABCD is parallelogram, then
2(AB)2 + 2(BC)2 = (AC)2 + (BD)2
In case of rectangle and square, this law reduces to Pythagoras theorem.