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### Maths MCQ Class IX Ch-8 | Quadrilaterals

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__Mathematics__

## MCQ | Class 09 | Chapter 8

__Quadrilaterals__

**MCQ Based on the different Quadrilaterals.**

**MCQ Based on the different Quadrilaterals.****MCQ Based on the concept of Properties of Quadrilaterals.**

**MCQ Based on the concept of Properties of Quadrilaterals.****MCQ Based on the differentiating different types of quadrilaterals.**

**MCQ Based on the differentiating different types of quadrilaterals.**__Features__

__Features__

**In the MCQ given below you find the important MCQ which are strictly according to the CBSE syllabus and are very useful for the CBSE Examinations.****Solution Hints are also given to some difficult problems.****Each MCQ contains four options from which one option is correct.**

__Action Plan__

__Action Plan__

**First of all students should Learn and write all basic points and Formulas related to the Chapter 8 Quadrilaterals.****Start solving the NCERT Problems with examples.****Solve the important assignments on the Chapter 8 Class XI.****Then start solving the following MCQ.**

# MCQ | CHAPTER - 8 | CLASS IX

QUADRILATERAL

**Q1) 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

Answer:** b**

Q2) Quadrilateral has __________ sides.

a) one

b) two

c) three

d) four

**
**

Answer:** ** d

**Q3) The sum of all the angles of a quadrilateral
is equal to:**

a) 180°

b) 270°

c) 360°

d) 90°

Answer:** c**

Q4) The sum of four angles of quadrilateral is equal
to _______

a) 90°

b) 360°

c) 180°

d) 270°

**
**

Answer:** ** b

**Q5) A trapezium has:**

a) One pair of opposite sides parallel

b) Two pairs of opposite sides parallel to each other

c) All its sides are equal

d) All angles are equal

Answer:** a**

Q6) Find the value of x.

a) 105°

b) 50°

c) 60°

d) 90°

Answer:** ** a

**Q7) A
rhombus can be a:**

a) Parallelogram

b) Trapezium

c) Kite

d) Square

Answer:** d**

Q8) At which angle do diagonals of a rhombus bisects
each other?

a) 180°

b) 360°

c) 270°

d) 90°

**
**

Answer:** ** d

**Q9) A diagonal of a parallelogram divides it
into two congruent:**

a) Square

b) Parallelogram

c) Triangles

d) Rectangle

Answer:** c**

Q10) What is the quadrilateral formed by the angle
bisectors of a parallelogram?

a) Square

b)
Rectangle

c) Circle

d) Rhombus

**
**

Answer:** ** b

**Q11) In a parallelogram, opposite angles are:**

a) Equal

b) Unequal

c) Cannot be determined

d) None of the above

Answer:** a**

Q12) Find the value of x if PQRS is a parallelogram.

a) 150°

b) 50°

c) 60°

d) 120°

**
**

Answer:** ** c

**Q13) The diagonals of a parallelogram are**

a) Equal

b) Unequal

c) Bisect each other

d) Have no relation

Answer:** c**

**Q14) From the figure find
the length of AD if perimeter of parallelogram ABCD is 26cm.
**

a) 10 cm

b) 15 cm

c) 12 cm

d) 5 cm

Answer:** ** d

**Q15) Each angle of the rectangle is:**

a) More than 90°

b) Less than 90°

c) Equal to 90°

d) Equal to 45°

Answer:** c**

**Q16) 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°

Answer:** b**

**Explanation:**

**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°**

**Q17) 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

Answer:** a**

**Explanation : See Q12 Exercise 8.1 NCERT**

**Q18)
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.

Answer: **c**

Q19) If the ratio of four angles of a quadrilateral is ∠A : ∠B : ∠C : ∠D = 1 : 2 : 3 : 4, what
is the value of ∠C?

a) 90°

b) 108°

c) 180°

d) 72°

**
**

Answer:** ** b

**Q20) Three angles of a quadrilateral are 75Âº,
90Âº and 75Âº. The fourth angle is**

a) 90Âº

b) 95Âº

c) 105Âº

d) 120Âº

Answer: **d**

**Explanation:
We know that the sum of angles of a quadrilateral is 360Âº.**

**Let the
unknown angle be x.**

**Therefore,
75Âº + 90Âº + 75Âº + x = 360Âº**

**x = 360Âº –
240Âº = 120Âº.**

Q21) What is the length of
DE if DE || BC and D and E are midpoints of AB and AC?

a) 18cm

b) 15cm

c) 9cm

d) 20cm

Answer:** ** c (9 cm)

**Q22) ABCD is a rhombus such that ****∠****ACB = 40Âº. Then ****∠****ADB is**

(a) 40Âº

(b) 45Âº

(c) 50Âº

(d) 60Âº

Answer: **c**

**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 = 180Âº**

**(where
∠BOC= 90Âº, ∠OCB = 40Âº)**

**90Âº + 40Âº + ∠OBC = 180Âº**

**∠OBC = 180Âº – 130Âº**

**∠OBC = 50Âº**

**∠OBC =∠DBC**

**Now, by
using alternate angles, we can say**

**∠ADB = 50Âº**

Q23) Find the perimeter of Î”ABC, if perimeter of Î”PQR is 36cm and A, B and C are midpoints.

a) 9cm

b) 18cm

c) 20cm

d) 36cm

Answer:** ** b

**Q24) 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: **d**

**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.**

**Q25) A diagonal of a
parallelogram divides it into two congruent:**

a. Square

b. Parallelogram

c. Triangles

d. Rectangle

**
**

Answer c

**Q26) A diagonal of a rectangle is inclined to
one side of the rectangle at 25Âº. The acute angle between the diagonals is**

a) 25Âº

b) 40Âº

c) 50Âº

d) 55Âº

Answer: **c**

**Explanation:
Consider the rectangle ABCD**

**In a
triangle BOC, **

**∠OBC = ∠OCB (Opposite angles of isosceles triangle)**

**Therefore, ∠OBC + ∠OCB + ∠BOC = 180Âº**

**25Âº + 25Âº + ∠BOC = 180Âº**

**∠BOC = 180Âº- 50Âº**

**∠BOC = 130Âº.**

**By using
the linear pair, **

**∠AOB + ∠BOC = 180Âº**

**∠AOB = 180Âº – 130Âº**

**∠AOB= 50Âº**

**Hence, the
acute angle between the diagonals is 50Âº.**

**Q27) In a parallelogram,
opposite angles are:**

a. Equal

b. Unequal

c. Cannot be determined

d. None of the above

Answer a

**Q28) If angles A, B, C and D of the quadrilateral
ABCD, taken in order, are in the ratio 3 : 7 : 6 : 4, then ABCD is a**

a) Kite

b) Rhombus

c)
Parallelogram

d) Trapezium

Answer: **d**

**Explanation: Given that,
the angles A, B, C and D of a quadrilateral are in the ratio 3 : 7 : 6 : 4.**

**We know
that A + B + C + D = 360Âº**

**Hence, now
we can assume, 3x + 7x + 6x + 4x = 360Âº**

**20x = 360Âº**

**x=18Âº**

**Therefore,
A = 3x = 54Âº**

**B = 7x =
126Âº**

**C = 6x =
108Âº**

**D = 4x= 72Âº**

**Here ∠A + ∠B = 180 ^{o}**

** ⇒ AD ॥ BC**

**And ∠C + ∠D = 180 ^{o}**

** ⇒ AD ॥ BC**

**⇒ ABCD is a quadrilateral with
one pair of opposite sides are parallel.**

**⇒ ABCD is a trapezium**

**Q29) 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

Answer: **c**

**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.**

**Q30) Each angle of rectangle
is:**

a. More than 90°

b. Less than 90°

c. Equal to 90°

d. Equal to 45°

Answer c

**Q31) The figure obtained by joining the
mid-points of the sides of a rhombus, taken in order, is**

a) a square

b) a rhombus

c) a
rectangle

d) any
parallelogram

Answer: **c**

**Explanation:
See Q2 NCERT Ex- 8.2**

**Let ABCD be
a rhombus. P, Q, R, S be the midpoint of the sides AB, BC, CD and DA. If we
join the midpoints, we will get the shape rectangle.**

**Q32) If APB and CQD are two parallel lines, then
the bisectors of the angles APQ, BPQ, CQP and PQD form**

a) Square

b) Rectangle

c) Rhombus

d) any
other parallelogram

Answer:** b**

**Explanation: Hence, the
bisectors of the angles APQ, BPQ, CQP and PQD form the shape rectangle.**

**Q33) Which of the following is not a
quadrilateral?**

a) Kite

b) Square

c) Triangle

d) Rhombus

Answer: **c**

**Download Math MCQ Worksheet For Class IX**

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