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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)kite
- c)rectangle
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Which of the following quadrilaterals has two pairs of adjacent sides ...
Kite, is a quadrilaterals has two pairs of adjacent sides equal and diagonals intersecting at right angles.
Most Upvoted Answer
Which of the following quadrilaterals has two pairs of adjacent sides ...
Key Concepts:
- Quadrilaterals are polygons with four sides.
- A square is a quadrilateral with four equal sides and four right angles.
- A rhombus is a quadrilateral with four equal sides, but the angles are not necessarily right angles.
- A kite is a quadrilateral with two pairs of adjacent sides equal, but the angles are not necessarily right angles.
- A rectangle is a quadrilateral with four right angles, but the sides are not necessarily equal.
Explanation:
To determine which quadrilateral has two pairs of adjacent sides equal and diagonals intersecting at right angles, we need to analyze the properties of each quadrilateral: square, rhombus, kite, and rectangle.
Square:
- A square has four equal sides and four right angles.
- The diagonals of a square intersect at right angles.
- Therefore, a square satisfies the given conditions.
Rhombus:
- A rhombus has four equal sides, but the angles are not necessarily right angles.
- The diagonals of a rhombus intersect at non-right angles.
- Therefore, a rhombus does not satisfy the given conditions.
Kite:
- A kite has two pairs of adjacent sides equal, but the angles are not necessarily right angles.
- The diagonals of a kite intersect at non-right angles.
- Therefore, a kite does not satisfy the given conditions.
Rectangle:
- A rectangle has four right angles, but the sides are not necessarily equal.
- The diagonals of a rectangle intersect at right angles.
- Therefore, a rectangle satisfies the given conditions.
Conclusion:
Based on the analysis above, the quadrilateral that has two pairs of adjacent sides equal and diagonals intersecting at right angles is a square.
- Quadrilaterals are polygons with four sides.
- A square is a quadrilateral with four equal sides and four right angles.
- A rhombus is a quadrilateral with four equal sides, but the angles are not necessarily right angles.
- A kite is a quadrilateral with two pairs of adjacent sides equal, but the angles are not necessarily right angles.
- A rectangle is a quadrilateral with four right angles, but the sides are not necessarily equal.
Explanation:
To determine which quadrilateral has two pairs of adjacent sides equal and diagonals intersecting at right angles, we need to analyze the properties of each quadrilateral: square, rhombus, kite, and rectangle.
Square:
- A square has four equal sides and four right angles.
- The diagonals of a square intersect at right angles.
- Therefore, a square satisfies the given conditions.
Rhombus:
- A rhombus has four equal sides, but the angles are not necessarily right angles.
- The diagonals of a rhombus intersect at non-right angles.
- Therefore, a rhombus does not satisfy the given conditions.
Kite:
- A kite has two pairs of adjacent sides equal, but the angles are not necessarily right angles.
- The diagonals of a kite intersect at non-right angles.
- Therefore, a kite does not satisfy the given conditions.
Rectangle:
- A rectangle has four right angles, but the sides are not necessarily equal.
- The diagonals of a rectangle intersect at right angles.
- Therefore, a rectangle satisfies the given conditions.
Conclusion:
Based on the analysis above, the quadrilateral that has two pairs of adjacent sides equal and diagonals intersecting at right angles is a square.
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Community Answer
Which of the following quadrilaterals has two pairs of adjacent sides ...
Sum of all exterior angles of a regular polygon =360 .So number of sides here =360÷45=8.
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Which of the following quadrilaterals has two pairs of adjacent sides equal and diagonals intersecting at right angles?a)parallelogramb)kitec)rectangled)None of theseCorrect answer is option 'B'. Can you explain this answer?
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