Quadrilaterals Test

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Quadrilaterals Test - 1

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Weekly Quiz Competition

Question 1
1 / -0

The length of each side of a rhombus is 10cm and one of its diagonal is of length 16cm. The Length of the other Diagonal is:

A
13cm

B
6cm

C
5cm

D
12cm

Solution

Explanation:

Use pythagoras theorem in right triangle,

10² -[16/2]² = 100 -64 = 36 = [6]² ; hence the other diagonal = 6x2 = 12cm
Question 2
1 / -0

If ABCD is a Parallelogram with 2 Adjacent angles ∠A = ∠B, then the parallelogram is a

A
Triangle

B
Rhombus

C
Square

D
Rectangle

Solution

Explanation:

The sum of the adjacent angles of a parallelogram is 180⁰. Opposite sides of a parallelogram are equal. Hence it is a rectangle.
Question 3
1 / -0

If an angle of a parallelogram is two-third of its adjacent angle, the smallest angle of the parallelogram is:

A
81^∘

B
72^∘

C
108^∘

D
54^∘

Solution

Explanation:

Let x be one angle. Then x+2/3 x=180 {sum of the adjacent angles of a parallelogram is 180⁰}

x=108, adjacent angle= 180-108= 72⁰
Question 4
1 / -0

If area of a Parallelogram with sides ‘a’ and ‘b’ is A and that of a rectangle with sides ‘a’ and ‘b’ is B, then

A
A < B

B
A = B

C
None of these

D
A > B

Solution

Explanation:

Area of Parallelogram = Base * Height

if 'a' is the side and 'b' is the base the height will be less than 'a' ( using Pythagorus theorem, a as Hypotenuse, h as height )

A < B
Question 5
1 / -0

The Parallel sides of a trapezium are ‘a’ and ‘b’ res. The line joining the mid-points of its non-parallel sides will be

A
None of These

B
1/2 (a-b)

C
1/2 (a+b)

D
2ab/(a+b)
Question 6
1 / -0

Two parallelograms stand on same base and between the same parallels. The ratio of their areas is

A
It is 1:1

B
It is 1:2

C
It is 2:1

D
It is 3:1

Solution

Explanation:

Parallelograms on the same base and between the same parallels are equal in area. Hence the ration of two parallelograms will be 1:1.
Question 7
1 / -0

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 of the statement/statements is/areTrue?

A
I and II

B
I and III

C
II

D
I

Solution

Explanation:

I. The adjacent angles of a parallelogram are supplementary. Their halves add up to 90^o . so the angle bisectors enclose a right angle.

II. All the adjacent angle bisectors enclose right angles.Sowehave a rectangle being enclosed by the angle bisectors of a parallelogram.

III. The triangle formed by joining the mid-points of the sides of an isosceles triangle is always an isosceles triangle, because halves of equal sides are also equal
Question 8
1 / -0

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 ∠A as well as ∠C.

Which is True?

A
II

B
I

C
III

D
II and III
Question 9
1 / -0

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?

A
52cm

B
51cm

C
20cm

D
80cm
Question 10
1 / -0

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

A
Rectangle

B
Parallelogram

C
Square

D
Triangle

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Re-Attempt Weekly Quiz Competition

Quadrilaterals Test - 1

Result

Quadrilaterals Test - 1

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Rank

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SHARING IS CARING

Question 1

13cm

6cm

5cm

12cm

Solution

Question 2

Triangle

Rhombus

Square

Rectangle

Solution

Question 3

81∘

72∘

108∘

54∘

Solution

Question 4

A < B

A = B

None of these

A > B

Solution

Question 5

None of These

1/2 (a-b)

1/2 (a+b)

2ab/(a+b)

Question 6

It is 1:1

It is 1:2

It is 2:1

It is 3:1

Solution

Question 7

I and II

I and III

II

I

Solution

Question 8

II

I

III

II and III

Question 9

52cm

51cm

20cm

80cm

Question 10

Rectangle

Parallelogram

Square

Triangle

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81^∘

72^∘

108^∘

54^∘