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This mock test of Test: Quadrilaterals- 2 for Class 9 helps you for every Class 9 entrance exam.
This contains 25 Multiple Choice Questions for Class 9 Test: Quadrilaterals- 2 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

Two parallelogram stand on equal bases and between the same parallels. The ratio of their areas is

Solution:

QUESTION: 2

In quadrilateral ABCD, if ∠A = 60^{∘} and ∠B : ∠C : ∠D = 2:3:7, then ∠D is :

Solution:

QUESTION: 3

D and E are the mid-points of the sides AB and AC res. Of △ABC. DE is produced to F. To prove that CF is equal and parallel to DA, we need an additional information which is:

Solution:

QUESTION: 4

P, Q, R are the mid- points of AB, BC, AC res, If AB = 10cm, BC = 8cm, AC = 12cm, Find the perimeter of △PQR.

Solution:

QUESTION: 5

In Triangle ABC which is right angled at B. Given that AB = 9cm, AC = 15cm and D, E are the mid-points of the sides AB and AC res. Find the length of BC?

Solution:

QUESTION: 6

Three Statements are given below:

(I) In a, Parallelogram the angle bisectors of 2 adjacent angles enclose a right angle.

(II) The angle bisector of a Parallelogram form a Rectangle.

(III) The Triangle formed by joining the mid-points of the sides of an isosceles triangle is not necessarily an isosceles triangle. Which is True?

Solution:

QUESTION: 7

If APB and CQD are 2 parallel lines, then the bisectors of the angles APQ, BPQ, CQP and PQD form, square only if

Solution:

Line APB is parallel to CQD

when we join PQ it will be transversal

then angleBPQ=angleCQP (alternate angles)

angleAPQ=anglePQD

when we will draw bisectors

then the figure formed will have opposite angles equal

which means that it is a parallelogram

QUESTION: 8

If bisectors of ∠A and ∠B of a quadrilateral ABCD intersect each other at P, of ∠B and ∠C at Q, of ∠C and ∠D at R and of ∠D and ∠A at S, then PQRS is a

Solution:

To show: ∠PSR + ∠PQR = 180°

∠SPQ + ∠SRQ = 180°

In △DSA,

∠DAS + ∠ADS + ∠DSA = 180° (angle sum property)

+ ∠ SA = 180° (since RD and AP are bisectors of ∠D and ∠A)

∠DSA = 180°

∠PSR = 180°−

(∵ ∠DSA = ∠PSR are vertically opposite angles)

Similarly,

∠PQR = 180°−

Adding (i) and (ii), we get, ∠PSR + ∠PQR = 180°

=360° − 1/2 × (∠A + ∠B + ∠C + ∠D)

=360°− 1/2 × 360° = 180° ∴ ∠PSR + ∠PQR = 180°

In quadrilateral PQRS,

∠SPQ + ∠SRQ + ∠PSR + ∠PQR = 360°

=> ∠SPQ + ∠SRQ + 180° = 360°

=> ∠SPQ + ∠SRQ = 180°

Hence, showed that opposite angles of PQRS are supplementary.

QUESTION: 9

The Diagonals AC and BD of a Parallelogram ABCD intersect each other at the point O such that ∠DAC = 30^{∘} and ∠AOB = 70^{∘}. Then, ∠DBC?

Solution:

QUESTION: 10

In Parallelogram ABCD, bisectors of angles A and B intersect each other at O. The measure of ∠AOB is

Solution:

QUESTION: 11

Three statements are given below:

(I) In a Rectangle ABCD, the diagonals AC bisects ∠A as well as ∠C.

(II) In a Square ABCD, the diagonals AC bisects ∠A as well as ∠C.

(III) In rhombus ABCD, the diagonals AC bisects ∠Aas well as ∠C.

Which is True?

Solution:

QUESTION: 12

D and E are the mid-points of the sides AB and AC of △ABC and O is any point on the side BC, O is joined to A. If P and Q are the mid-points of OB and OC res, Then DEQP is

Solution:

QUESTION: 13

Given Rectangle ABCD and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA res. If length of a diagonal of Rectangle is 8cm, then the quadrilateral PQRS is a

Solution:

QUESTION: 14

In the given figure, ABCD is a Rhombus. Then,

Solution:

QUESTION: 15

D and E are the mid-points of the sides AB and AC. Of △ABC. If BC = 5.6cm, find DE.

Solution:

QUESTION: 16

In a triangle P, Q and R are the mid-points of the sides BC, CA and AB res. If AC = 21cm, BC = 29cm and AB = 30cm, find the perimeter of the quadrilateral ARPQ?

Solution:

QUESTION: 17

The bisectors of the angles of a Parallelogram enclose a

Solution:

QUESTION: 18

Opposite angles of a Quadrilateral ABCD are equal. If AB = 4cm, find the length of CD.

Solution:

QUESTION: 19

In a Trapezium ABCD, if AB ║ CD, then (AC^{2}+ BD^{2}) = ?

Solution:

QUESTION: 20

In quadrilateral ABCD, ∠B=90^{∘}, ∠C−∠D = 60^{∘} and ∠A−∠C−∠D = 10^{∘}. Find ∠A, ∠C and ∠D.

Solution:

QUESTION: 21

If a Quadrilateral ABCD,∠A = 90^{∘} and AB = BC = CD = DA, Then ABCD is a

Solution:

QUESTION: 22

Rhombus is a quadrilateral

Solution:

QUESTION: 23

In △ABC, EF is the line segment joining the mid-points of the sides AB and AC. BC = 7.2cm, Find EF.

Solution:

QUESTION: 24

In the figure, ABCD is a rhombus, whose diagonals meet at 0. Find the values of x and y.

Solution:

Since diagonals of a rhombus bisect each other at right angle .

∴ In △AOB , we have

∠OAB + ∠x + 90° = 180°

∠x = 180° - 90° - 35° [∵ ∠OAB = 35°]

= 55°

Also, ∠DAO = ∠BAO = 35°

∴ ∠y + ∠DAO + ∠BAO + ∠x = 180°

⇒ ∠y + 35° + 35° + 55° = 180°

⇒ ∠y = 180° - 125° = 55°

Hence the values of x and y are x = 55°, y = 55°.

QUESTION: 25

The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O. If ∠DAC = 32^{∘} and ∠AOB = 70^{∘} then, ∠DBC is equal to

Solution:

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