Understanding Quadrilaterals(8th Grade > Mathematics ) Questions and answers for exam Preparation

8th Grade > Mathematics

UNDERSTANDING QUADRILATERALS MCQs

Total Questions : 464 | Page 7 of 47 pages

Question 61. A quadrilateral has two of its angles as

30^{\circ}

and

40^{\circ}

. What type of quadrilateral can it be?

Trapezium
Square
Parallelogram
Rectangle

Discuss Question

Answer: Option A. -> Trapezium
:
A
In square and rectangle each angle is

90^{0}

.
In a parallelogram, two adjacent angles have to be either equal or supplementary. The angles

30^{\circ}

and

40^{\circ}

are neither supplementary nor equal. So, the twoangles cannot belong to a parallelogram.
Fortrapezium, there are no such restrictions. So, the given qudrilateral is a trapezium.

Question 62. I draw a quadrilateral and then draw all its diagonals.How many triangles can I find?

Discuss Question

Answer: Option C. -> 8
:
C

I Draw A Quadrilateral And Then Draw All Its Diagonals.How M...

The triangles are-

Δ A B D, Δ C B D, Δ A B C, Δ D C A, Δ A E D, Δ C E D, Δ B E C, Δ A E B

⟹

There are 8 triangles in the figure.

Question 63. The number of sides in a kite is
___.

Discuss Question

:
A kite is a quadrilateral. Hence it has 4 sides.

Question 64. In parallelogram ABCD, which of the 2 sides are equal?

AB & BC
AB & AD
CD & BC
AB & CD

Discuss Question

Answer: Option D. -> AB & CD
:
D
The opposite sides of a parallelogram are equal.
Hence, sides AB & CD (if the cyclic order of the vertices are A, B, C, D) are opposite sides and are equal.

In Parallelogram ABCD, Which Of The 2 Sides Are Equal?

Question 65. Which of the following is not true for the figure below?

AC ⊥ BD
ABCD is a kite
∠ADB = ∠ABD
∠DAB = ∠DCB

Discuss Question

Answer: Option D. -> ∠DAB = ∠DCB
:
D

It is given that AB = AD and BC = CD.
Since, two pairs of adjacent sides are equal, the ABCD is a kite.
According to the properties of a kite:

A C ⊥ B D

[Diagonals of kite are perpendicular.]
In

Δ A B D,

∠ A D B

∠ A B D

[∵ B A = D A

and angles opposite to equal sidesare equal

]

But,

∠ D A B

\neq

∠ D C B

Question 66. Find

∠ A B F

from the given figure.

30∘
45∘
60∘
75∘

Discuss Question

Answer: Option C. -> 60∘
:
C

∠ B C D + ∠ B C H = 180^{\circ}

[ Linear pair]

∠ B C D

180^{\circ}

35^{\circ}

145^{\circ}

In quadrilateral BEDC,

∠ B E D

∠ E D C

∠ D C B

∠ C B E

360^{\circ}

∠ C B E

360^{\circ}

- (

105^{\circ}

50^{\circ}

145^{\circ}

) =

60^{\circ}

So,

∠ A B F

∠ C B E

60^{\circ}

(Vertically opposite angles)

Question 67. What is the measure of any exterior angle of a regular nonagon?

40∘
100∘
140∘
90∘

Discuss Question

Answer: Option A. -> 40∘
:
A
Sum of the exterior angles of a polygon (irrespective of the number of sides) is

360^{\circ}

.
In a nonagon, the measure of all exterior angles will be the same i.e.

360^{\circ}

.
Also, nonagon has 9 sides.
So, measure of each exteriorangle
=

\frac{360^{\circ}}{9} = 40^{\circ}

Question 68. The diagonal of a parallelogram divides it into two congruent triangles.

True
False
140∘
90∘

Discuss Question

Answer: Option A. -> True
:
A

The Diagonal Of A Parallelogram Divides It Into Two Congruen...

Δ A B D

and

Δ C D B

AB = CD (Opposite sides of a parallelogram)
AD = CB (Opposite sides of a parallelogram)
BD = DB (Common)
So,

Δ A B D

≅

Δ C D B

(By SSS congruence condition)

Question 69. The total number of parallelograms in this figure is
___

Discuss Question

:
Rectangles are also parallelograms. They are shown in color "blue" in the below figures. Hence, there are 7parallelograms in the figure.

Question 70. Which of the following quadrilaterals has/have equal length of diagonals?
i) Rhombus
ii) Rectangle
iii) Square
iv) Kite
v) Parallelogram

i, ii, iii
ii, iii
ii, iii, v
ii, iii, iv

Discuss Question

Answer: Option B. -> ii, iii
:
B
Rhombus has unequal diagonals which are perpendicular bisectors.
Square has equal diagonals which are perpendicular bisectors.
Rectangle has equal diagonals which are perpendicular bisectors .
Kite has unequal diagonals in which the longer one bisects the other.
Parallelogram has unequal diagonals unless it is a square or a rectangle. The diagonals bisect each other.