Question

what is a parallelogram? Define the characteristics of a parallelogram and satisfy the condition required for the same?
Answer it in detail.​

Answer 1

parallelogram = a four-sided plane rectilinear figure with opposite sides parallel.

Condition #1: If one pair of opposite sides are. parallel and congruent, then the quadrilateral is. a parallelogram.

Condition #2: If both pairs of opposite sides are congruent, then the quadrilateral is a parallelogram.

Answer 2

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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. 

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.

Conditions satisfying the criteria of a parallelogram :-

● Both pairs of opposite sides are parallel.

● Both pairs of opposite sides are congruent.

● Both pairs of opposite angles are congruent.

● Diagonals bisect each other.

● One angle is supplementary to both consecutive angles (same-side interior).