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?

Question

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?

Answer

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.

Answer

Rhombus

PROPERTIES OF RHOMBUS

1. all sides are equal
2. opposite sides are equal and parallel
3. opposite angles are equal
4. diagonals bisect each other perpendicular

so according to the question

the properties 1 and 4 refers to the given question

so the answer is rhombus

Answer

This property holds for kites, rhombuses and squares all

Answer

B ans

Answer

Good question

Answer

Rhombus has 4 side equal length
so, the adjacent side are equal
a square is also a rhombus . so, the diagonals are interesting at right angle

Answer

Rectangle is right answer

Answer

It is rhombus
AB=DC
BC=AD
opposite sides are equal
diagnols bisect each other at 90 degree
in a rhombus diagonals bisect each other because rhombus are also parallelograms
OA=OC
OB=OD
IN TRIANGLE AOB AND AOD WE HAVE
AB=AD(SIDES OF A RHOMBUS ARE EQUAL)
OB=OD
OA=OA(COMMON)
BY SSS WE HAVE
TRIANGLE AOB IS CONGRUENT TO TRIANGLE AOD
ANGLE AOB = ANGLE AOD
AOB+AOD=180 DEGREE (LINEAR PAIR)
AOB+AOB=180
2AOB=180
AOB=90
AOB=AOD=90 DEGREE
HENCE PROVED

Answer

D) rectangle.

Answer

Rhombus

Answer

Answer B

Answer

B

Answer

Rhombus has all its sides of equal length and hence, the adjacent sides of rhombus are equal as well.
Rhombus has a property by which the diagonals are perpendicular bisectors of each other.
Therefore, Correct answer is a rhombus.

Answer

The answer is (c)kite as it has two pairs of adjacent sides and has diagonals perpendicular to each other.

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