Understanding Quadrilaterals Test

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Understanding Quadrilaterals Test - 4

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following statements is CORRECT?

A
The diagonals of a parallelogram are equal.

B
The diagonals of a rectangle are perpendicular to each other.

C
If the diagonals of a quadrilateral intersect at right angles, it is not necessarily a rhombus.

D
Every quadrilateral is either a trapezium or a parallelogram or a kite.
Question 2
1 / -0

Four angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. The difference between the greatest and the smallest angle is

A
125^∘

B
75^∘

C
108^∘

D
120^∘

Solution

Let the angles be x, 2x, 3x and 4x.
Sum of the angles of a quadrilateral = 360^∘
= x + 2x + 3x + 4x = 360^∘
⇒ 10x = 360∘
⇒ x = 36^∘
∴ Required difference = 4x − x = 3x = 3 × 36^∘ = 108^∘
Question 3
1 / -0

A trapezium in which non-parallel Sides are equal is said to be _____.

A
Right trapezium

B
Equilateral trapezium

C
Isosceles trapezium

D
None of these
Question 4
1 / -0

Which of the following can never be the measure of exterior angle of a regular polygon?

A
22^∘

B
36^∘

C
45^∘

D
30^∘
Question 5
1 / -0

The quadrilateral having only one pair of opposite sides parallel is called a____ .

A
Square

B
Rhombus

C
Trapezium

D
Parallelogram
Question 6
1 / -0

The theatre in the town is built in the form of a kite. Its perimeter is 100 m. If one of its sides is 20 m, what are the lengths of other sides?

A
20m, 30m, 30m

B
30m, 40m, 40m

C
20m, 40m, 32m

D
30m, 40m, 50m

Solution

Let ABCD be the theatre in which AB = AD = 20 m and let SC = CD = x m
Perimeter of the theatre =100 m
⇒ 100 = AB + BC + CD + DA 100
= (20 + x + x + 20)m
⇒ 40 + 2x = 100
⇒ (20 + x) = 50
⇒ x = 30m
So, AB = AD = 20 m
and
BC = CD = 30 m
Question 7
1 / -0

Atul is playing in a playground which is of the form of a parallelogram. He observes that the diagonals of the playground are 80 m and 60 m long. So, the playground is in the shape of _____.

A
Rectangle

B
Rhombus

C
Kite

D
Square

Solution

In rectangle and square, diagonals are of equal length. Also, kite is not a parallelogram.

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Understanding Quadrilaterals Test - 4

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Question 1

The diagonals of a parallelogram are equal.

The diagonals of a rectangle are perpendicular to each other.

If the diagonals of a quadrilateral intersect at right angles, it is not necessarily a rhombus.

Every quadrilateral is either a trapezium or a parallelogram or a kite.

Question 2

125∘

75∘

108∘

120∘

Solution

Question 3

Right trapezium

Equilateral trapezium

Isosceles trapezium

None of these

Question 4

22∘

36∘

45∘

30∘

Question 5

Square

Rhombus

Trapezium

Parallelogram

Question 6

20m, 30m, 30m

30m, 40m, 40m

20m, 40m, 32m

30m, 40m, 50m

Solution

Question 7

Rectangle

Rhombus

Kite

Square

Solution

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125^∘

75^∘

108^∘

120^∘

22^∘

36^∘

45^∘

30^∘