Understanding Quadrilaterals Test

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Understanding Quadrilaterals Test - 11

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Weekly Quiz Competition

Question 1
1 / -0

If each pair of opposite sides of a quadrilateral are equal and parallel, then it is a ____________.

A
Kite

B
Trapezium

C
Parallelogram

D
None of these

Solution

if each pair of opposite sides of a quadrilateral is equal and parallel then it is a parallelogram (property of parallelogram)
Question 2
1 / -0

Two opposite angles of a parallelogram are $${\left( {3x - 2} \right)^ \circ }$$ and $${\left( {50 - x} \right)^ \circ }$$. Find the value of $$x$$

A
$$61$$

B
$$13$$

C
$$64$$

D
$$67$$

Solution

Two opposite angles of a parallelogram are $$(3x-2)^o$$ and $$(50-x)^o$$
We know that, opposite angles of parallelogram are equal.
$$\therefore$$ $$3x-2=50-x$$
$$\Rightarrow$$ $$3x+x=50+2$$
$$\Rightarrow$$ $$4x=52$$
$$\Rightarrow$$ $$x=13$$
$$\therefore$$ The value of $$x$$ is $$13^o$$
Question 3
1 / -0

The measure of an angle of a parallelogram is $$70^0$$. Its remaining angles are:

A
$$110^0,\,110^0 \text{ and } 70^0$$

B
$$110^0 , 70^0\text{ and }120^0$$

C
$$110^0 , 80^0\text{ and }120^0$$

D
$$90^0 , 70^0\text{ and }120^0$$

Solution

Let $$\angle A, \angle B, \angle C,\angle D$$ be the four angles of the parallelogram ABCD, Such that $$\angle B$$ and $$\angle D$$ are opposite angles and also $$\angle A$$ and $$\angle C $$ are the opposite angles.
Let $$\angle A = 70^o$$, then $$\angle C=70^o$$ {opposite angles are equal}
Angle adjacent to $$\angle A = \angle D=180^o-70^o$$
$$=110^o$$
Also, $$\angle D = \angle B = 110^o$$ {Opposite angles}
$$So\>angles\>are\>70^\circ,110^\circ,70^\circ,110^\circ\>(complete\>set)$$
Question 4
1 / -0

What values of $$a$$ would make the given quadrilateral a parallelogram.

A
$$5 \dfrac{1}{4}$$

B
$$ \dfrac{11}{2}$$

C
$$5 \dfrac{3}{4}$$

D
$$5$$

Solution

As the diagonal of quadrilateral bisects each other; 5b-4=3b+6
2b=10
$$b=5$$
So by the same rule;3b-4=2a
15-4=2a
11=2a
$$a=\dfrac{11}{2}$$
Question 5
1 / -0

Boundaries of surfaces are:

A
surfaces

B
curves

C
lines

D
points

Solution

Boundaries of surfaces are curves.
Hence, (b) is the correct answer.
Question 6
1 / -0

ABCD is a parallelogram and X is the mid-point of AB. If $$Area(\Box AXCD) = $$ $$24$$ $${cm}^2$$, Find $$Area(\Delta ABC) $$.

A
$$16$$ $$ cm^2$$

B
$$26$$ $$ cm^2$$

C
$$12$$ $$ cm^2$$

D
$$24$$ $$ cm^2$$

Solution

Given-
$$ ABCD$$ is a parallelogram and X is mid point of AB.
$$A(\Box AXCD)={ 24 cm }^{ 2 }$$
To find out-
The statement $$A(\Delta ABC)={ 24 cm }^{ 2 }$$ is true or false.
Solution-
Let the altitude of $$\Box ABCD=h.$$
Now, $$AB\parallel DC$$ i.e $$AX\parallel DC$$
So, $$\Box AXCD$$ is a trapezium.
Also, $$AX=BX$$ i.e $$AB=2AX$$ .....(i)
$$ \therefore A(\Box AXCD)=\cfrac { 1 }{ 2 } \times h\times (DC+AX)={ 24cm }^{ 2 }$$ ....(ii)
And, $$A(\Delta ABC=\cfrac { 1 }{ 2 } \times h\times AB=\cfrac { 1 }{ 2 } \times h\times 2AX={ 24cm }^{ 2 }$$ .....(iii)
From (ii) & (iii) we have,
$$ \cfrac { 1 }{ 2 } \times h\times (DC+AX)=\cfrac { 1 }{ 2 } \times h\times AB= \cfrac { 1 }{ 2 } \times h\times 2AX$$ ...(from i)
$$(DC+AX)=2AX\Longrightarrow DC=AX$$
But $$DC=AB$$
$$\therefore AB=AX. $$
It is impossible as AX is a part of AB.
So, $$A(\Delta ABC) \neq { 24cm }^{ 2 }$$
Ans- False
Question 7
1 / -0

In the above figure, it is given that $$BDEF$$ and $$FDCE$$ are parallelograms. Can you say that $$BD = CD$$? Why or why not?

A
Yes

B
No

C
May be

D
Cannot be determined

Solution

Given:-
$$ABC$$ is a triangle. $$D,\;E\;F$$ are points on $$BC,\;CA.\;AB$$ taken in order. $$BDEF$$ anf $$FDCE$$ are parallelograms.

To Prove:-
$$BD=CD$$

Proof:-
In parallelogram $$BDEF$$,
$$BD=EF\quad\quad\quad\dots(i)$$[Opposite sides of a parallelogram are equal.]

In parallelogram $$FDCE$$,
$$CD=EF\quad\quad\quad\dots(ii)$$[Opposite sides of a parallelogram are equal.]

From $$(i)$$ and $$(ii)$$,
$$BD=CD$$

Hence, proved.
Question 8
1 / -0

All the angles of a quadrilateral are equal. What special name is given to this quadrilateral?

A
Rectangle

B
Trapezium

C
Rhombus

D
Parallelogram

Solution

We know that the sum of the angles of the quadrilateral is $$360^{o}$$
Now, the quadrilateral in given question has all angles equal.
$$ \therefore$$ Each angle $$={ 360 }^{ o }\div 4={ 90 }^{ o }$$
So, this quadrilateral would be rectangle or a square.
Question 9
1 / -0

Opposite angles of a quadrilateral $$ABCD$$ are equal. If $$AB = 4$$ cm, determine $$CD$$.

A
$$3$$ cm

B
$$4$$ cm

C
$$5$$ cm

D
$$6$$ cm

Solution

Let $$ABCD$$ be a quadrilateral.
Given, opposite angles of a quadrilateral $$ABCD$$ are equal.
So, opposite sides of the quadrilateral $$ABCD$$ are equal.
$$\Rightarrow AB=CD$$
Given, $$AB=4$$ cm
Therefore, $$CD=4$$ cm.
Question 10
1 / -0

Which of the following is not always true for a parallelogram?

A
Opposite sides are equal.

B
Opposite angles are equal.

C
Opposite angles are bisected by the diagonals.

D
Diagonals bisect each other.

Solution

Opposite angles are bisected by the diagonals.
The above statement is not true for every parallelogram.
It is true only for a rhombus (diamond) or square where the diagonals bisect the opposite angles they connect, and diagonals are perpendicular. In rectangles, the diagonals do not bisect the angles and are not perpendicular, but they do bisect each other.

Hence, option C.

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Re-Attempt Weekly Quiz Competition

Understanding Quadrilaterals Test - 11

Result

Understanding Quadrilaterals Test - 11

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SHARING IS CARING

Question 1

Kite

Trapezium

Parallelogram

None of these

Solution

Question 2

$$61$$

$$13$$

$$64$$

$$67$$

Solution

Question 3

$$110^0,\,110^0 \text{ and } 70^0$$

$$110^0 , 70^0\text{ and }120^0$$

$$110^0 , 80^0\text{ and }120^0$$

$$90^0 , 70^0\text{ and }120^0$$

Solution

Question 4

$$5 \dfrac{1}{4}$$

$$ \dfrac{11}{2}$$

$$5 \dfrac{3}{4}$$

$$5$$

Solution

Question 5

surfaces

curves

lines

points

Solution

Question 6

$$16$$ $$ cm^2$$

$$26$$ $$ cm^2$$

$$12$$ $$ cm^2$$

$$24$$ $$ cm^2$$

Solution

Question 7

Yes

No

May be

Cannot be determined

Solution

Question 8

Rectangle

Trapezium

Rhombus

Parallelogram

Solution

Question 9

$$3$$ cm

$$4$$ cm

$$5$$ cm

$$6$$ cm

Solution

Question 10

Opposite sides are equal.

Opposite angles are equal.

Opposite angles are bisected by the diagonals.

Diagonals bisect each other.

Solution

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