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If a quadrilateral has equal diagonals but unequal and non-parallel adjacent sides, then which of the following quadrilaterals can it be?
- a)Parallelogram
- b)Rhombus
- c)Isosceles trapezium
- d)Kite
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
If a quadrilateral has equal diagonals but unequal and non-parallel a...
To determine which quadrilateral can have equal diagonals but unequal and non-parallel adjacent sides, we need to analyze the properties of each option: a) parallelogram, b) rhombus, c) isosceles trapezium, and d) kite.
1. Parallelogram:
A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. The diagonals of a parallelogram bisect each other, meaning they divide each other into two equal parts. Since the adjacent sides are unequal and non-parallel, a quadrilateral with these properties cannot be a parallelogram.
2. Rhombus:
A rhombus is a quadrilateral with all sides of equal length. The diagonals of a rhombus bisect each other at right angles, meaning they divide each other into two equal parts. However, since the adjacent sides are unequal and non-parallel, a quadrilateral with these properties cannot be a rhombus.
3. Isosceles Trapezium:
An isosceles trapezium is a quadrilateral with two parallel sides (the bases) and two non-parallel sides (the legs) with equal length. The diagonals of an isosceles trapezium are equal in length. Moreover, the adjacent sides are unequal and non-parallel, satisfying the given conditions. Therefore, a quadrilateral with these properties can be an isosceles trapezium.
4. Kite:
A kite is a quadrilateral with two pairs of adjacent sides that are equal in length. The diagonals of a kite intersect at right angles, but they are not necessarily equal in length. Therefore, a quadrilateral with equal diagonals but unequal and non-parallel adjacent sides cannot be a kite.
Hence, the correct answer is option 'C' - isosceles trapezium.
1. Parallelogram:
A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. The diagonals of a parallelogram bisect each other, meaning they divide each other into two equal parts. Since the adjacent sides are unequal and non-parallel, a quadrilateral with these properties cannot be a parallelogram.
2. Rhombus:
A rhombus is a quadrilateral with all sides of equal length. The diagonals of a rhombus bisect each other at right angles, meaning they divide each other into two equal parts. However, since the adjacent sides are unequal and non-parallel, a quadrilateral with these properties cannot be a rhombus.
3. Isosceles Trapezium:
An isosceles trapezium is a quadrilateral with two parallel sides (the bases) and two non-parallel sides (the legs) with equal length. The diagonals of an isosceles trapezium are equal in length. Moreover, the adjacent sides are unequal and non-parallel, satisfying the given conditions. Therefore, a quadrilateral with these properties can be an isosceles trapezium.
4. Kite:
A kite is a quadrilateral with two pairs of adjacent sides that are equal in length. The diagonals of a kite intersect at right angles, but they are not necessarily equal in length. Therefore, a quadrilateral with equal diagonals but unequal and non-parallel adjacent sides cannot be a kite.
Hence, the correct answer is option 'C' - isosceles trapezium.
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If a quadrilateral has equal diagonals but unequal and non-parallel a...
The quadrilateral which has equal diagonals but unequal and non-parallel adjacent sides can be an isosceles trapezium.
ABCD is an isosceles trapezium, with AD = BC and AB parallel to DC. Diagonals AC and BD are equal.
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If a quadrilateral has equal diagonals but unequal and non-parallel adjacent sides, then which of the following quadrilaterals can it be?a)Parallelogramb)Rhombusc)Isosceles trapeziumd)KiteCorrect answer is option 'C'. Can you explain this answer?
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