Parallelogram
a quadrilateral whose opposite sides are both parallel and equal in length
A parallelogram is a quadrilateral with opposite sides parallel. This means that in a parallelogram, opposite sides are equal in length and opposite angles are congruent. The properties of a parallelogram can be more easily understood by drawing a diagram of the shape.
Properties of a parallelogram:
1. Opposite sides are parallel: This means that the sides of the parallelogram opposite to each other are parallel and equal in length.
2. Opposite angles are congruent: This means that the angles that are opposite to each other in the parallelogram are congruent.
3. Consecutive angles are supplementary: This means that the sum of any two consecutive angles in the parallelogram is 180 degrees.
4. Diagonals bisect each other: The diagonals of a parallelogram bisect each other. This means that they divide each other into two equal parts.
5. Area of a parallelogram: The area of a parallelogram is equal to the product of its base and height. The base of a parallelogram is any one of its sides and the height is the perpendicular distance between the base and the opposite side of the parallelogram.
6. The sum of the squares of the four sides of a parallelogram is equal to the sum of the squares of its diagonals.
Applications of parallelogram:
1. Construction of geometrical structures: The properties of a parallelogram are useful in constructing geometrical structures such as buildings, bridges, and roads.
2. In engineering and construction: Parallelograms are used extensively in engineering and construction for the design of structures like support beams, trusses, and frames.
3. In navigation: The properties of a parallelogram are used in navigation to determine the position of a vessel relative to its desired course.
4. In physics: Parallelograms are used in physics to calculate vectors and forces acting on objects.
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