Test: Quadrilaterals- 2 - Class 9 MCQ

# Test: Quadrilaterals- 2 - Class 9 MCQ

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## 25 Questions MCQ Test Mathematics (Maths) Class 9 - Test: Quadrilaterals- 2

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Test: Quadrilaterals- 2 - Question 1

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

Test: Quadrilaterals- 2 - Question 2

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

Test: Quadrilaterals- 2 - 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:

Test: Quadrilaterals- 2 - 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.

Test: Quadrilaterals- 2 - 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?

Test: Quadrilaterals- 2 - 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?

Test: Quadrilaterals- 2 - 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

Detailed Solution for Test: Quadrilaterals- 2 - Question 7
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

Test: Quadrilaterals- 2 - 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

Detailed Solution for Test: Quadrilaterals- 2 - Question 8

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°

∠SPQ + ∠SRQ + ∠PSR + ∠PQR = 360°
=> ∠SPQ + ∠SRQ + 180° = 360°
=> ∠SPQ + ∠SRQ = 180°

Hence, showed that opposite angles of PQRS are supplementary.

Test: Quadrilaterals- 2 - 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?

Test: Quadrilaterals- 2 - Question 10

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

Test: Quadrilaterals- 2 - 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?

Test: Quadrilaterals- 2 - 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

Test: Quadrilaterals- 2 - 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

Test: Quadrilaterals- 2 - Question 14

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

Test: Quadrilaterals- 2 - Question 15

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

Test: Quadrilaterals- 2 - 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?

Test: Quadrilaterals- 2 - Question 17

The bisectors of the angles of a Parallelogram enclose a

Test: Quadrilaterals- 2 - Question 18

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

Test: Quadrilaterals- 2 - Question 19

In a Trapezium ABCD, if AB ║ CD, then (AC2+ BD2) = ?

Test: Quadrilaterals- 2 - Question 20

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

Test: Quadrilaterals- 2 - Question 21

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

Test: Quadrilaterals- 2 - Question 22

Test: Quadrilaterals- 2 - Question 23

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

Test: Quadrilaterals- 2 - Question 24

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

Detailed Solution for Test: Quadrilaterals- 2 - Question 24

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°.

Test: Quadrilaterals- 2 - 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

## Mathematics (Maths) Class 9

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## Mathematics (Maths) Class 9

48 videos|378 docs|65 tests