Question

all rules and formula of parallelogram​

Answer 1

If anyone of the angles is a right angle, then all the other angles will be the right angle. The two diagonals bisect each other. Each diagonal bisects the parallelogram into two congruent triangles. Sum of square of all the sides of parallelogram is equal to the sum of square of its diagonals.

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Answer 2

Answer:

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A parallelogram is a two-dimensional geometrical shape, whose sides are parallel to each other. It is a type of polygon having four sides (also called quadrilateral), where the pair of parallel sides are equal in length. Also, the interior opposite angles of a parallelogram are equal in measure. Sum of adjacent angles of a parallelogram is equal to 180 degrees. 

A three-dimensional shape has its faces in parallelogram shape, is called parallelepiped. The area of parallelogram depends on the base (one its parallel side) and height (altitude drawn from top to bottom) of it. The perimeter of parallelogram depends on the length of its four sides.

In geometry, you must have learned about many 2D shapes and sizes such as circle, square, rectangle, rhombus, etc. All of these shapes have a different set of properties. Also, the area and perimeter formulas of these shapes vary with each other and are used to solve many problems. Let us learn here the definition, formulas and properties of a parallelogram.

Parallelogram Definition

A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length, and the opposite angles are equal in measure. Also, the interior angles on the same side of the transversal are supplementary. Sum of all the interior angles equals 360 degrees.

A square and a rectangle are two shapes which have similar properties of a parallelogram.

Rhombus: If all the sides of a parallelogram are congruent or equal to each other, then it is a rhombus.

If there is one parallel side and the other two sides are non-parallel, then it is a trapezium.

In the figure above, you can see, ABCD is a parallelogram, where AB || CD and AD || BC. 

Also, AB = CD and AD = BC

And, ∠A = ∠C & ∠B = ∠D

Also, ∠A & ∠D are supplementary angles because these interior angles lie on the same side of the transversal. In the same way, ∠B & ∠C are supplementary angles.

Therefore,

∠A + ∠D = 180

∠B + ∠C = 180

Shape of Parellelogram

A parallelogram is a two-dimensional shape. It has four sides, in which two pairs of sides are parallel. Also, the parallel sides are equal in length.

If the length of the parallel sides is not equal in measurement, then the shape is not a parallelogram. Similarly, the opposite interior angles of parallelogram should always be equal. Otherwise, it is not a parallelogram.

Special Parallelograms

Square and Rectangle: A square and a rectangle are two shapes which have similar properties of a parallelogram. Both have their opposite sides equal and parallel to each other. Diagonals of both the shapes bisect each other. 

Rhombus: If all the sides of a parallelogram are congruent or equal to each other, then it is a rhombus.

Rhomboid: A special case of a parallelogram that has its opposite sides parallel to each other but adjacent sides are of unequal lengths. Also, the angles are equal to 90 degrees.

Trapezium: If there is one parallel side and the other two sides are non-parallel, then it is a trapezium. 

Angles of Parallelogram

A parallelogram is a flat 2d shape which has four angles. The opposite interior angles are equal. The angles on the same side of the transversal are supplementary, that means they add up to 180 degrees. Hence, the sum of the interior angles of a parallelogram is 360 degrees.

Properties of Parallelogram

If a quadrilateral has a pair of parallel opposite sides, then it’s a special polygon called Parallelogram. The properties of a parallelogram are as follows:

• The opposite sides are parallel and congruent

• The opposite angles are congruent

• The consecutive angles are supplementary

• If anyone of the angles is a right angle, then all the other angles will be the right angle

• The two diagonals bisect each other

• Each diagonal bisects the parallelogram into two congruent triangles

• Sum of square of all the sides of parallelogram is equal to the sum of square of its diagonals. It is also called parallelogram law