Which among the following quadrilaterals posses all sides as congruent, all angles bring right angled and opposite sides being parallel respectively.

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Rectangle

Square

Trapezium

Rhombus

answer is B.

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Detailed Solution

We need to find a quadrilateral that can satisfy the properties as, all sides are congruent, all angles are right angles and opposite sides are parallel respectively.
All side lengths corresponding to a quadrilateral which are equal, are said to be congruent.
Now, we will use this fact and decide which of the mentioned quadrilaterals hold the properties as mentioned in the question.
So, if we consider the first property, i.e., ‘all sides are congruent’, then there are two such quadrilaterals whose all sides are congruent, viz., a rhombus and a square.
Next, if we consider the second property, i.e., ‘all angles are right angles’, then out of rhombus and square, only square has all its interior angles as right angles.
Next, if we consider the last property, i.e., opposite sides are parallel, then again square holds this property since it is a parallelogram.
So, based on the above analysis, we conclude that a square is the quadrilateral in which all the sides are congruent, all the interior angles are right angles and the opposite side pairs are parallel.
Hence, the correct option is (2).

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