Class 9 Maths MCQ Questions of Quadrilaterals are made available here with answers. The questions here are prepared, consistent with the CBSE syllabus. Students can brace oneself for their exams with the assistance of those objective questions to score good marks. The answers here are available with detailed explanations.
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Types of Quadrilaterals
There are various types of quadrilaterals. The word ‘Quad’ means four, and every one these sorts of quadrilaterals have four sides, the sum of the angles of those shapes is 360 degrees.
- Trapezium
- Parallelogram
- Squares
- Rectangle
- Rhombus
- Kite
Solve the MCQ Questions given below with four multiple options and choose the correct one from them. Given below are MCQ Questions of Quadrilaterals. There are a total of 20 Multiple Choice Questions on Quadrilaterals.
Practice MCQ Questions for Class 9 Maths
1. The quadrilateral whose all its sides are equal and angles are equal to 90 degrees, it is called:
(a) Rectangle
(b) Square
(c) Kite
(d) Parallelogram
2. The sum of all the angles of a quadrilateral is equal to:
(a) 180°
(b) 270°
(c) 360°
(d) 90°
3. A trapezium has:
(a) One pair of opposite sides parallel
(b) Two pair of opposite sides parallel to each other
(c) All its sides are equal
(d) All angles are equal
4. A rhombus can be a:
(a) Parallelogram
(b) Trapezium
(c) Kite
(d) Square
5. A diagonal of a parallelogram divides it into two congruent:
(a) Square
(b) Parallelogram
(c) Triangles
(d) Rectangle
6. If the bisectors of all four angles of a parallelogram are made to intersect each other then the new quadrilateral thus formed will be a:
(a) Rhombus
(b) Rectangle
(c) Square
(d) Parallelogram
7. A square is a special type of
(a) Rectangle
(b) Rhombus
(c) Parallelogram
(d) All of the above
8. Which of the following is/are the necessary condition(s) for a quadrilateral to be a parallelogram?
(a) Its diagonals bisect each other.
(b) Opposite angles are equal.
(c) Opposite sides are equal and parallel to each other
(d) All of the above
9. In a parallelogram, opposite angles are:
(a) Equal
(b) Unequal
(c) Cannot be determined
(d) None of the above
10. The diagonals of a parallelogram:
(a) Equal
(b) Unequal
(c) Bisect each other
(d) Have no relation
11. Each angle of the rectangle is:
(a) More than 90°
(b) Less than 90°
(c) Equal to 90°
(d) Equal to 45°
12. The angles of a quadrilateral are in the ratio 4: 5: 10: 11. The angles are:
(a) 36°, 60°, 108°, 156°
(b) 48°, 60°, 120°, 132°
(c) 52°, 60°, 122°, 126°
(d) 60°, 60°, 120°, 120°
13. If ABCD is a trapezium in which AB || CD and AD = BC, then:
(a) ∠A = ∠B
(b) ∠A > ∠B
(c) ∠A < ∠B
(d) None of the above
14. Three angles of a quadrilateral are 75°, 90°and 75°, the fourth angle is
(a) 90°
(b) 95°
(c) 105°
(d) 120°
15. The diagonals of rhombus are 12 cm and 16 cm. The length of the side of rhombus is:
(a) 12 cm
(b) 16 cm
(c) 8 cm
(d) 10 cm
16. Which of the following is not true for a parallelogram?
(a) Opposite sides are equal
(b) Opposite angles are equal
(c) Opposite angles are bisected by the diagonals
(d) Diagonals bisect each other.
17. ABCD is a rhombus such that ∠ACB = 40º. Then ∠ADB is
(a) 40º
(b) 45º
(c) 50º
(d) 60º
18. Which of the following is not a quadrilateral?
(a) Kite
(b) Square
(c) Triangle
(d) Rhombus
19. The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rectangle, if
(a) PQRS is a rectangle
(b) PQRS is a parallelogram
(c) Diagonals of PQRS are perpendicular
(d) Diagonals of PQRS are equal
20. The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rhombus, if
(a) PQRS is a rhombus
(b) PQRS is a parallelogram
(c) Diagonals of PQRS are perpendicular
(d) Diagonals of PQRS are equal.
Answer:
1. Answer: (b) Square
2. Answer: (c) 360°
3. Answer: (a) One pair of opposite sides parallel
Explanation: A trapezium has only one pair of opposite sides parallel to each other and other two sides are non-parallel.
4. Answer: (d) Square
5. Answer: (c) Triangles
6. Answer: (b) Rectangle
7. Answer: (d) All of the above
8. Answer: (d) All of the above
9. Answer: (a) Equal
10. Answer: (c) Bisect each other
11. Answer: (c) Equal to 90°
Explanation: Let ABCD is a rectangle, and ∠A = 90°
AD || BC and AB is a transversal
∠ A + ∠ B = 180° (Interior angles on the same side of the transversal)
∠ A = 90°
So, ∠ B = 180° – ∠ A = 180° – 90° = 90°
Now, ∠ C = ∠ A and ∠ D = ∠ B (Opposite angles of the parallelogram)
So, ∠ C = 90° and ∠ D = 90°
Hence all sides are equals to 90°.
12. Answer: (b) 48°, 60°, 120°, 132°
Explanation: Let x be the common angle among all the four angles of a quadrilateral.
As per angle sum property, we know:
4x+5x+10x+11x = 360°
30x = 360°
x = 12°
Hence, angles are
4x = 4 (12) = 48°
5x = 5 (12) = 60°
10x = 10 (12) = 120°
11x = 11 (12) = 132°
13. Answer: (a) ∠A = ∠B
Explanation: Draw a line through C parallel to DA intersecting AB produced at E.
CE = AD (Opposite sides)
AD = BC (Given)
BC = CE
⇒ ∠CBE = ∠CEB
also,
∠A + ∠CBE = 180° (Angles on the same side of transversal and ∠CBE = ∠CEB)
∠B + ∠CBE = 180° ( As Linear pair)
⇒ ∠A = ∠B
14. Answer: (d) 120°
Explanation: We know, by angle sum property, the sum of angles of a quadrilateral is 360°.
The given angles are,
Let the fourth angle be x°
Then, 75° + 90° + 75° + x° = 360°
⇒ 360° – (75° + 90° + 75°) =x°
⇒ x = 360° – 240° = 120°.
15. Answer: (d) 10 cm
Explanation: Diagonals of rhombus are cut each other at 90.
Since d1 = 16 and d2 =12
Therefore, by Pythagoras theorem
a2 = (d1/2)2 + (d2/2)2
⇒ a2 = 82 + 62
⇒ a = √100 = 10
16. Answer: (c) Opposite angles are bisected by the diagonals
Explanation: Opposite angles are bisected by the diagonals is not true for a parallelogram. Whereas opposite sides are equal, opposite angles are equals, diagonals bisect each other are the properties of a parallelogram.
17. Answer: (c) 50º
Explanation: We know that the diagonals of the rhombus bisect each other perpendicularly.
By using the alternate interior angles, and angle sum property of triangle, we can say:
From the triangle, BOC,
∠BOC + ∠OCB + ∠OBC = 180º
(where ∠BOC= 90º, ∠OCB = 40º)
90º+40º+ ∠OBC = 180º
∠OBC = 180º – 130º
∠OBC = 50º
∠OBC =∠DBC
Now, by using alternate angles, we can say
∠ADB = 50º
18. Answer: (c) Triangle
Explanation: square, kite and rhombus are quadrilaterals as it has four sides. Whereas a triangle is not a quadrilateral as it has only three sides.
19. Answer: (c) Diagonals of PQRS are perpendicular
Explanation: The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rectangle, if the diagonals of PQRS are perpendicular.
20. Answer: (d) Diagonals of PQRS are equal.
Explanation: The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rhombus if the diagonals of PQRS are equal.
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