What is a Parallelogram
In this session I am going to tell you about What is a Parallelogram. Parallelogram in mathematics is a part of Euclidean geometry. It is basically a convex quadrilateral having two pairs of sides which are parallel to each other. In a parallelogram the opposite angles are equal and the opposite sides are equal in length. In a parallelogram the three dimensional counterpart is a parallelepiped. A parallelogram is a shape which has 4 sides, in which two pairs of sides are equal in length, similarly in rectangle. Angles can be of 90 degrees as in rectangle but it is not necessary.
If we push a rectangle with its four sides and flex point then it starts lean over and now the right angles at the corners are not right now, but we still have a parallelogram having 4 sides with two pairs of equal sides.
Here I am going to discuss the characteristics of the parallelogram which are as follows:
A convex quadrilateral is a parallelogram if it has one of the following characteristic
1. Diagonals of the parallelogram divide the quadrilateral into two congruent triangles.
2. Opposite sides of a parallelogram are equal.
3. Diagonals of the parallelogram always bisect each other.
4. Also in a parallelogram the opposite angles are always equal.
5. Always follow the parallelogram low, according to which the sum of the square of the sides is equal to the square of the diagonal of the parallelogram.
Now here are some properties of the parallelogram:
1. Any line which passes through the midpoint of a parallelogram bisect the whole area covered.
2. Perimeter of the parallelogram is 2(x + y) here x, y are the lengths of adjacent facings.
3. The opposite sides of a parallelogram never intersect because sides are parallel by definition.
4. If we create the triangle in a parallelogram by its diagonal then the square of the area of triangle is equal to the area of parallelogram.
5. The area is the magnitude of the vector cross product of adjacent facings of the parallelogram.
A parallelogram has several types which are as follows:
1. Rhomboid: In a rhomboid parallelogram opposite sides are always parallel and adjacent sides can never be equal. It also doesn’t have any right angles.
2. Rectangle: It has four angles which have equal size.
3. Rhombus: It has four sides of equal length.
4. Square: This parallelogram has four edges or sides which are equal and four angles known as right angles and are equal in size.
5. The area K of the parallelogram to the right (the blue area) is the total area of the rectangle less the area of the two orange triangles.
We can calculate the area of a parallelogram by using the formula given below:
Area = Area of rectangle – 2* Area of triangle
Here the area of rectangle is R = (Br + An)*Hi
And the area of triangle is T = ½ *An * Hi
Then the area of parallelogram becomes:
P = R – 2*T
= ((Br + An)*Hi) – (An*Hi)
= Br *Hi
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