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

8th Grade > Mathematics

UNDERSTANDING QUADRILATERALS MCQs

Total Questions : 464 | Page 8 of 47 pages

Question 71. Square is a regular quadrilateral.

True
False
140∘
90∘

Discuss Question

Answer: Option A. -> True
:
A
A polygon is called a regular polygon if it is equiangular and equilateral. i.e., All the angles are equal and measure of all the sides are equal.
Square is quadrilateral with all the angles equal to

90^{\circ}

and all the sides of equal length.

⟹

Square is a regular quadrilateral.
Hence, the given statement is true.

Question 72. ABCD is a parallelogram in which

∠ D C B

and

∠ A B C

are in ratio 2:7. Find the sum of

∠ A B D

and

∠ A D B

ABCD Is A Parallelogram In Which ∠DCB And ∠ABC Are In Ra...

40∘
50∘
70∘
140∘

Discuss Question

Answer: Option D. -> 140∘
:
D

∠ D C B + ∠ A B C = 180^{\circ}

[Adjacent angles of a parallelogram are supplementary]

\Rightarrow 2 t + 7 t = 180^{\circ}

[

∵ ∠ D C B

and

∠ A B C

are in ratio 2:7]

\Rightarrow t = 20^{\circ}

∴ ∠ D C B = 2 t = 2 \times 20^{\circ} = 40^{\circ}

and

∠ A B C = 7 t = 7 \times 20^{\circ} = 140^{\circ}

Now,

∠ D A B = ∠ D C B = 40^{\circ}

[Opposite angles of a parallelogram are equal]

∠ D A B + ∠ A D B + ∠ A B D = 180^{\circ}

[Sum of the angles of a triangle]

\Rightarrow 40^{\circ} + ∠ A D B + ∠ A B D = 180^{\circ}

\Rightarrow ∠ A D B + ∠ A B D = 140^{\circ}

Question 73.
If a diagonal of a quadrilateral bisects both the angles, then it is a
a) Kite
b) Parallelogram
c) Rhombus
d) Rectangle

Discuss Question

:
If a diagonal of a quadrilateral bisects both the angles, then it is a rhombus.

Question 74.
In parallelogram ABCD, the angle bisector of

∠ A

bisects BC. Will angle bisector of B also bisect AD? Give reason.

Discuss Question

:
Given, ABCD is a parallelogram, bisector of

∠ A

, bisects BC at F, i.e.

∠ 1 = ∠ 2

, CF = FB.
Draw

F E ∥ B A

ABFE is a parallelogram by construction [

∵ F E ∥ B A

]

\Rightarrow ∠ 1 = ∠ 6

[alternate angle]

In Parallelogram ABCD, The Angle Bisector Of ∠A Bisects BC...

But

∠ 1 = ∠ 2

[given]

∴ ∠ 2 = ∠ 6

AB = FB [opposite sides to equal angles are equal] ..... (i)

∴ A B F E i s a r h o m b u s

.
Now, in

Δ A B O

and

Δ B O F

, AB = BF [from Eq. (i)]
BO = BO [common]
AO = FO [diagonals of rhombus bisect each other]

∴ Δ A B O ≅ Δ B O F

[by SSS]

∠ 3 = ∠ 4

[by CPCT]
Now,

B F = \frac{1}{2} B C

[given]

\Rightarrow B F = \frac{1}{2} A D

[BC = AD]

\Rightarrow A E = \frac{1}{2} A D

[BF = AE]

∴

E is the mid-point of AD.

Question 75.
A parallelogram can be constructed uniquely, if both diagonals and the angle between them is given.

Discuss Question

:
True
We can draw a unique parallelogram, if both diagonals and the angle between them is given.

A Parallelogram Can Be Constructed Uniquely, If Both Diagona...

Question 76.
Which of the following is an equiangular and equilateral polygon?
a) Square
b) Rectangle
c) Rhombus
d) Right angled Triangle

Discuss Question

:
In a square, all the sides and all the angles are equal.
Hence, square is an equiangular and equilateral polygon.

Question 77.
All rectangles are parallelograms.

Discuss Question

:
True
Rectangles are special parallelograms and satisfy all properties of parallelograms. Therefore, we can say that all rectangles are parallelograms but vice-versa is not true.

Question 78.
Two angles of a quadrilateral are each of measure