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Which of the following quadrilaterals has two pairs of adjacent sides equal and diagonals intersecting at right angles?
- a)Parallelogram
- b)rhombus
- c)Triangle
- d)rectangle
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Which of the following quadrilaterals has two pairs of adjacent sides ...
Correct Answer :- b
Explanation:- A rhombus is a parallelogram and a quadrilateral whose opposite sides are parallel and opposite angles are equal.
Area of Rhombus, A = (d1 x d2)/2
The perimeter of Rhombus, P = 4a units
The opposite angles of a rhombus are equal to each other.
In a rhombus, diagonals bisecting each other at right angles.
Diagonals bisect the angles of a rhombus
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Community Answer
Which of the following quadrilaterals has two pairs of adjacent sides ...
Explanation:
A quadrilateral is a four-sided polygon. There are different types of quadrilaterals based on their properties. The given question asks us to identify a quadrilateral that has two pairs of adjacent sides equal and diagonals intersecting at right angles. Let's examine each option to see which one satisfies these conditions.
(A) Square: A square is a quadrilateral with four equal sides and four right angles. The diagonals of a square are equal and intersect at right angles. Therefore, a square satisfies the given conditions.
(B) Rhombus: A rhombus is a quadrilateral with four equal sides. The diagonals of a rhombus intersect at right angles, but they are not necessarily equal in length. However, since a rhombus has two pairs of adjacent sides equal, it satisfies the given conditions.
(C) Kite: A kite is a quadrilateral with two pairs of adjacent sides equal. However, the diagonals of a kite are not necessarily perpendicular to each other. Therefore, a kite does not satisfy the given conditions.
(D) Rectangle: A rectangle is a quadrilateral with four right angles. The diagonals of a rectangle intersect at right angles, but they are not necessarily equal in length. However, since a rectangle has two pairs of adjacent sides equal, it satisfies the given conditions.
Conclusion:
Out of the given options, only the rhombus and the square satisfy the given conditions. However, since the square is a special case of the rhombus where all angles are right angles, we can say that the answer is option B, which is a rhombus.
A quadrilateral is a four-sided polygon. There are different types of quadrilaterals based on their properties. The given question asks us to identify a quadrilateral that has two pairs of adjacent sides equal and diagonals intersecting at right angles. Let's examine each option to see which one satisfies these conditions.
(A) Square: A square is a quadrilateral with four equal sides and four right angles. The diagonals of a square are equal and intersect at right angles. Therefore, a square satisfies the given conditions.
(B) Rhombus: A rhombus is a quadrilateral with four equal sides. The diagonals of a rhombus intersect at right angles, but they are not necessarily equal in length. However, since a rhombus has two pairs of adjacent sides equal, it satisfies the given conditions.
(C) Kite: A kite is a quadrilateral with two pairs of adjacent sides equal. However, the diagonals of a kite are not necessarily perpendicular to each other. Therefore, a kite does not satisfy the given conditions.
(D) Rectangle: A rectangle is a quadrilateral with four right angles. The diagonals of a rectangle intersect at right angles, but they are not necessarily equal in length. However, since a rectangle has two pairs of adjacent sides equal, it satisfies the given conditions.
Conclusion:
Out of the given options, only the rhombus and the square satisfy the given conditions. However, since the square is a special case of the rhombus where all angles are right angles, we can say that the answer is option B, which is a rhombus.
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