Q. If a quadrilateral has one pair of parallel sides, it is classified as which type? (2023)
A.
Parallelogram
B.
Trapezium
C.
Rectangle
D.
Rhombus
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Solution
A quadrilateral with one pair of parallel sides is classified as a trapezium.
Correct Answer: B — Trapezium
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Q. If the area of a quadrilateral is given by the formula A = 1/2 * d1 * d2 * sin(θ), what do d1 and d2 represent? (2023)
A.
The lengths of the sides.
B.
The lengths of the diagonals.
C.
The lengths of the altitudes.
D.
The lengths of the bases.
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Solution
In the formula for the area of a quadrilateral, d1 and d2 represent the lengths of the diagonals.
Correct Answer: B — The lengths of the diagonals.
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Q. If the diagonals of a quadrilateral bisect each other, which of the following can be concluded? (2023)
A.
The quadrilateral is a rectangle.
B.
The quadrilateral is a rhombus.
C.
The quadrilateral is a parallelogram.
D.
The quadrilateral is a trapezium.
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Solution
If the diagonals of a quadrilateral bisect each other, it is a property of parallelograms.
Correct Answer: C — The quadrilateral is a parallelogram.
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Q. If the lengths of the diagonals of a rhombus are 10 cm and 24 cm, what is the area of the rhombus?
A.
120 cm²
B.
240 cm²
C.
60 cm²
D.
300 cm²
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Solution
The area of a rhombus can be calculated using the formula (1/2) × d1 × d2 = (1/2) × 10 × 24 = 120 cm².
Correct Answer: B — 240 cm²
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Q. In a cyclic quadrilateral, the opposite angles are related in which way? (2023)
A.
They are equal.
B.
They are supplementary.
C.
They are complementary.
D.
They are independent.
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Solution
In a cyclic quadrilateral, the opposite angles are supplementary, meaning they add up to 180 degrees.
Correct Answer: B — They are supplementary.
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Q. In a parallelogram, if one angle measures 60 degrees, what is the measure of the opposite angle?
A.
60 degrees
B.
120 degrees
C.
90 degrees
D.
180 degrees
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Solution
In a parallelogram, opposite angles are equal, so the opposite angle also measures 60 degrees.
Correct Answer: A — 60 degrees
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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 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. 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 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 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 the property that its diagonals are equal in length? (2023)
A.
Square
B.
Rhombus
C.
Trapezium
D.
Kite
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Solution
A square has equal diagonals, which is a property of squares and rectangles.
Correct Answer: A — Square
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Q. Which of the following statements about a parallelogram is true? (2023)
A.
All sides are equal.
B.
Diagonals bisect each other.
C.
All angles are right angles.
D.
It has exactly one pair of parallel sides.
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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. Which of the following statements about a rectangle is true?
A.
All sides are equal
B.
Opposite sides are equal and all angles are 90 degrees
C.
Diagonals are perpendicular
D.
Only one pair of opposite sides is equal
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Solution
In a rectangle, opposite sides are equal and all angles are indeed 90 degrees.
Correct Answer: B — Opposite sides are equal and all angles are 90 degrees
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Q. Which quadrilateral has all sides equal but angles not necessarily equal? (2023)
A.
Square
B.
Rectangle
C.
Rhombus
D.
Trapezium
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Solution
A rhombus has all sides equal, but the angles are not necessarily equal.
Correct Answer: C — Rhombus
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