Q. In a parallelogram, which of the following properties holds true?
A.
All sides are equal.
B.
Diagonals bisect each other.
C.
All angles are right angles.
D.
Only opposite angles are equal.
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Solution
In a parallelogram, the diagonals bisect each other, which is a defining property of parallelograms.
Correct Answer:
B
— Diagonals bisect each other.
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Q. In a parallelogram, which of the following properties is NOT true?
A.
Opposite angles are equal.
B.
Adjacent angles are supplementary.
C.
All sides are equal.
D.
Diagonals bisect each other.
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Solution
In a parallelogram, while opposite angles are equal and diagonals bisect each other, all sides being equal is a property of a rhombus, not all parallelograms.
Correct Answer:
C
— All sides are equal.
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Q. In a quadrilateral ABCD, if AB = CD and AD = BC, which of the following can be concluded?
A.
ABCD is a rectangle.
B.
ABCD is a parallelogram.
C.
ABCD is a trapezium.
D.
ABCD is a square.
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Solution
If both pairs of opposite sides are equal, then ABCD is a parallelogram.
Correct Answer:
B
— ABCD is a parallelogram.
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Q. In a quadrilateral ABCD, if angle A is 70 degrees and angle B is 110 degrees, what can be inferred about angles C and D?
A.
They must be equal.
B.
They must be supplementary.
C.
They can be any values.
D.
They must be complementary.
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Solution
The sum of the angles in a quadrilateral is 360 degrees. Therefore, angles C and D must sum to 180 degrees, making them supplementary.
Correct Answer:
B
— They must be supplementary.
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Q. In a quadrilateral ABCD, if angle A is 70 degrees and angle B is 110 degrees, what can be inferred about the sum of angles C and D?
A.
C and D must be 100 degrees
B.
C and D must be 180 degrees
C.
C and D must be 90 degrees
D.
C and D must be 360 degrees
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Solution
The sum of the angles in any quadrilateral is 360 degrees. Given angles A and B, we can find C + D = 360 - (70 + 110) = 180 degrees.
Correct Answer:
B
— C and D must be 180 degrees
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Q. In a quadrilateral ABCD, if angle A is 90 degrees and angle B is 45 degrees, what can be inferred about the other angles? (2023)
A.
Angle C is 45 degrees and angle D is 90 degrees.
B.
Angle C is 90 degrees and angle D is 45 degrees.
C.
Angle C is 135 degrees and angle D is 135 degrees.
D.
Angle C is 180 degrees and angle D is 0 degrees.
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Solution
In a quadrilateral, the sum of the angles is 360 degrees. Given angle A (90) and angle B (45), angle C + angle D = 360 - (90 + 45) = 225 degrees. The only option that fits is angle C = 135 degrees and angle D = 135 degrees.
Correct Answer:
C
— Angle C is 135 degrees and angle D is 135 degrees.
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Q. In a quadrilateral ABCD, if the sum of the interior angles is 360 degrees, which of the following statements is true?
A.
ABCD is a rectangle.
B.
ABCD can be any shape.
C.
ABCD must be a square.
D.
ABCD is a triangle.
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Solution
The sum of the interior angles of any quadrilateral is always 360 degrees, which means ABCD can be any shape that satisfies this condition.
Correct Answer:
B
— ABCD can be any shape.
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Q. In a quadrilateral, if one angle is 90 degrees and the opposite angle is 90 degrees, what can be concluded about the quadrilateral?
A.
It is a rectangle.
B.
It is a square.
C.
It is a parallelogram.
D.
It is a trapezium.
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Solution
If a quadrilateral has two opposite angles of 90 degrees, it must be a rectangle.
Correct Answer:
A
— It is a rectangle.
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Q. In a quadrilateral, if the lengths of all sides are equal, which of the following is true?
A.
It is a rectangle.
B.
It is a rhombus.
C.
It is a square.
D.
It can be any quadrilateral.
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Solution
If all sides of a quadrilateral are equal, it is a rhombus, but it can also be a square if the angles are right.
Correct Answer:
B
— It is a rhombus.
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Q. In a quadrilateral, if the sum of the interior angles is 360 degrees, which of the following statements is true?
A.
It can only be a rectangle.
B.
It can be a triangle.
C.
It can be any four-sided figure.
D.
It can only be a square.
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Solution
The sum of the interior angles of any quadrilateral is always 360 degrees, which applies to all four-sided figures.
Correct Answer:
C
— It can be any four-sided figure.
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Q. In a rectangle, which of the following is true about the diagonals? (2023)
A.
They are perpendicular.
B.
They are equal and bisect each other.
C.
They are unequal.
D.
They do not bisect each other.
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Solution
In a rectangle, the diagonals are equal in length and bisect each other.
Correct Answer:
B
— They are equal and bisect each other.
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Q. In a rhombus, what can be said about the angles?
A.
All angles are equal
B.
Opposite angles are equal
C.
Adjacent angles are equal
D.
All angles are right angles
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Solution
In a rhombus, opposite angles are equal.
Correct Answer:
B
— Opposite angles are equal
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Q. In a rhombus, what can be said about the diagonals?
A.
They are equal and bisect each other at right angles.
B.
They are unequal and bisect each other at right angles.
C.
They are equal and do not bisect each other.
D.
They are unequal and do not bisect each other.
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Solution
In a rhombus, the diagonals are unequal and bisect each other at right angles.
Correct Answer:
B
— They are unequal and bisect each other at right angles.
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Q. In a rhombus, what is the relationship between the lengths of the diagonals?
A.
They are equal
B.
They are perpendicular
C.
They bisect the angles
D.
Both B and C
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Solution
In a rhombus, the diagonals are perpendicular and they bisect the angles.
Correct Answer:
D
— Both B and C
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Q. In a square, if the length of one side is doubled, what happens to the area of the square?
A.
It remains the same
B.
It doubles
C.
It quadruples
D.
It increases by 50%
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Solution
If the side length of a square is doubled, the area increases by a factor of four (since area = side^2).
Correct Answer:
C
— It quadruples
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Q. In a trapezium, which of the following statements is true?
A.
All sides are equal.
B.
Only one pair of opposite sides is parallel.
C.
Both pairs of opposite sides are parallel.
D.
It has four right angles.
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Solution
In a trapezium, only one pair of opposite sides is parallel.
Correct Answer:
B
— Only one pair of opposite sides is parallel.
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Q. What is the area of a quadrilateral with vertices at (0,0), (4,0), (4,3), and (0,3)?
A.
12 square units
B.
10 square units
C.
15 square units
D.
20 square units
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Solution
The area can be calculated as length × width = 4 × 3 = 12 square units.
Correct Answer:
A
— 12 square units
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Q. What is the minimum number of sides a quadrilateral can have?
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Solution
A quadrilateral, by definition, has exactly four sides, so the minimum number of sides is 4.
Correct Answer:
C
— 4
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Q. What is the relationship between the sides of a rhombus?
A.
All sides are equal.
B.
Opposite sides are equal.
C.
Adjacent sides are equal.
D.
No sides are equal.
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Solution
In a rhombus, all sides are equal in length.
Correct Answer:
A
— All sides are equal.
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Q. What is the sum of the interior angles of a quadrilateral? (2023)
A.
180 degrees
B.
360 degrees
C.
540 degrees
D.
720 degrees
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Solution
The sum of the interior angles of any quadrilateral is 360 degrees.
Correct Answer:
B
— 360 degrees
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Q. Which of the following is NOT a property of a rhombus?
A.
All sides are equal
B.
Diagonals bisect each other at right angles
C.
Diagonals are equal in length
D.
Opposite angles are equal
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Solution
In a rhombus, while all sides are equal and diagonals bisect each other at right angles, the diagonals are not necessarily equal in length.
Correct Answer:
C
— Diagonals are equal in length
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Q. Which of the following is NOT a property of a square?
A.
All sides are equal
B.
Diagonals bisect each other
C.
Diagonals are equal in length
D.
All angles are acute
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Solution
In a square, all angles are right angles (90 degrees), not acute.
Correct Answer:
D
— All angles are acute
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Q. Which of the following quadrilaterals has all sides equal and opposite angles equal?
A.
Square
B.
Rectangle
C.
Trapezium
D.
Rhombus
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Solution
A rhombus has all sides equal and opposite angles equal.
Correct Answer:
D
— Rhombus
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Q. Which of the following quadrilaterals has diagonals that are equal in length but not perpendicular?
A.
Square
B.
Rectangle
C.
Rhombus
D.
Trapezium
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Solution
In a rectangle, the diagonals are equal in length but not perpendicular.
Correct Answer:
B
— Rectangle
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Q. Which of the following quadrilaterals has diagonals that are equal in length but not necessarily perpendicular?
A.
Rhombus
B.
Rectangle
C.
Trapezium
D.
Kite
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Solution
In a rectangle, the diagonals are equal in length but are not necessarily perpendicular.
Correct Answer:
B
— Rectangle
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Q. Which of the following quadrilaterals has diagonals that are equal in length?
A.
Rhombus
B.
Trapezium
C.
Rectangle
D.
Kite
Show solution
Solution
In a rectangle, the diagonals are equal in length.
Correct Answer:
C
— Rectangle
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Q. Which of the following quadrilaterals has diagonals that are not equal but bisect each other?
A.
Rectangle
B.
Square
C.
Rhombus
D.
Kite
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Solution
In a kite, the diagonals bisect each other but are not equal in length.
Correct Answer:
D
— Kite
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Q. Which of the following quadrilaterals has diagonals that are not equal in length?
A.
Square
B.
Rectangle
C.
Rhombus
D.
Kite
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Solution
A kite has diagonals that are not equal in length, while the others have equal diagonals.
Correct Answer:
D
— Kite
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Q. Which of the following quadrilaterals has diagonals that are not equal?
A.
Square
B.
Rectangle
C.
Rhombus
D.
Kite
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Solution
A kite has diagonals that are not equal, which distinguishes it from squares, rectangles, and rhombuses.
Correct Answer:
D
— Kite
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Q. Which of the following quadrilaterals has diagonals that bisect each other at right angles?
A.
Rectangle
B.
Square
C.
Rhombus
D.
Trapezium
Show solution
Solution
In a rhombus, the diagonals bisect each other at right angles.
Correct Answer:
C
— Rhombus
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