MCQ Questions for Class 9 Maths Quadrilaterals Quiz 1

Which of the following statements holds always?

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Every rectangle is a square.
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Every parallelogram is a trapezium.
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Every rhombus is a square.
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Every parallelogram is a rectangle.

Explanation

option

$A$
A square have all sides equal. A rectangle may have different adjacent but equal parallel sides.

So, rectangle can't be a square always.

option

$B$
A parallelogram is always a trapezium.

option

$C$

A rhombus does not always have angle of

$90^{o}$ always.

option

$D$

Parallelogram does not have all angles of

$90^{o}$ always.

Hence, option B is correct.

State true or false:

All squares are trapeziums.

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True
0%
False
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Ambiguous
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Data Insufficient

The value of

$x$ in the given diagram is ?

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$130^{o}$
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$140^{o}$
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$150^{o}$
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$160^{o}$

Explanation

$\textbf{Step 1: Find x using angle sum property.}$

$\text{The given angles are }70^o,60^o,90^o,x$ . $\textbf{[Linear pairs are supplementary]}$
$\text{Then, }70^o+60^o+90^o+x=360^o$ .

$\text{Therefore, the unknown angle is:}$

$\Rightarrow$ $360^o - (70^o + 60^o + 90^o ) =x$

$\Rightarrow$ $x=360^o - 220^o$

$=140^{\circ}$ .

$\text{Therefore, the unknown angle is }x=140^o$ .

$\textbf{Hence, option B is correct.}$

Can all the four angles of a quadrilateral be obtuse angle?

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Yes
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No
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May be
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Cannot be determined

Explanation

$\Rightarrow$ An obtuse angle is greater than

$90^o$ and by angle sum property, the sum of all four angles of a quadrilateral is

$360^o$ .

$\Rightarrow$ If we take all four angles greater than

$90^o$ then, there sum will be obviously greater than

$360^o$ .

Hence, all the four angles of a quadrilateral cannot be obtuse.

Therefore, option

$B$ is correct.

All rhombuses are parallelograms?

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True
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False
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Ambiguous
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Data Insufficient

State true or false:

Square have four right angles.

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True
0%
False

Explanation

A square is a quadrilateral which has 4 equal sides & angles.

Since, the sum of the angles of a quadrilateral is

${ 360 }^{ o }$ ,

Each angle

$=\cfrac { { 360 }^{ o } }{ 4 } ={ 90 }^{ o }$
Hence every square has four right angles.

If the diagonals AC and BD of a quadrilateral ABCD bisect each other, then ABCD is a :

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parallelogram
0%
rectangle
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rhombus
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trapezium

Explanation

The diagonals

$AC$ and

$BD$ of a quadrilateral

$ABCD$ bisect each other, then

$ABCD$ can be a parallelogram or any special type of parallelogram like rhombus, rectangle and square.
In a trapezium, the diagonals don't bisect each other.

State 'True' or 'False':

If two adjacent sides of a parallelogram are equal, it is a rhombus.

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True
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False

In a quadrilateral ABCD,

$\angle A + \angle C = 180^{\circ}$ then

$\angle B + \angle D =$

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$360^{\circ}$
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$100^{\circ}$
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$180^{\circ}$
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$80^{\circ}$

Explanation

We have,

$\angle A + \angle B + \angle C + \angle D = 360^{\circ}$

$(\angle A + \angle C) + (\angle B + \angle D) = 360^{\circ}$

$180^{\circ} + (\angle B + \angle D) = 360^{\circ}$

$\angle B + \angle D = 180^{\circ}$

A quadrilateral has ______ diagonals.

0%
1
0%
4
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2
0%
3

Explanation

We know that, a quadrilateral is a

$4-sided$ geometrical figure.

It has

$4$ vertices.

Hence, there are only

$2$ pairs of opposite (non-adjacent) vertices in a quadrilateral.

We also know that, a diagonal is a line segment joining two opposite (non-adjacent) vertices.

Therefore, a quadrilateral has

$2$ diagonals.

Which of the following is not true?

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A parallelogram having a pair of adjacent sides equal, is called a rhombus
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The diagonals of a rhombus do not bisect each other
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If the diagonals of a parallelogram bisect each other at right angles, it is a rhombus
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A rectangle is a parallelogram

Complete the following statement.

Number of measurements required to construct a square are__________.

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1
0%
2
0%
3
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4

Explanation

If we know the length of the side of the square, we can construct it since a square has all four sides equal and each of the four angles is equal to

${90}^{o}$

Hence, number of measurements required to construct a square is

$1$

Number of pairs of parallel lines in a trapezium is:

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$1$
0%
$2$
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$3$
0%
$4$

Explanation

A trapezium has one pair of parallel lines as shown in the figure. So option

$A$ is correct.

In which of the following figures the adjacent sides are not necessarily be equal?

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Parallelogram
0%
Rhombus
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Rectangle
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Square

Which of the following are equiangular and equilateral polygons?

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Square
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Rhombus
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Kite
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None of these

Find the angle measure x in the following figures

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$60^o$
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$50^o$
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$70^o$
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$80^o$

Explanation

Since the sum of angles (interior angles) of a quadrilateral is

$360^o$ .

$\therefore x + 120^o + 130^o + 50^o = 360^o$

$\Rightarrow x + 300^o = 360^o$

$\Rightarrow x= 360^o-300^o = 60^o$

The angle of a quadrilateral are respectively

$120^o, 73^o, 80^o$ . Find the fourth angle.

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$87^o$
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$85^o$
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$67^o$
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$57^o$

Explanation

Let the four angles be $\angle A , \angle B , \angle C$ and $\angle D$ .

Then $\angle A =120^o, \angle B=73^o , \angle C = 80^o$ .

We know, by angle sum property, the sum of angles of a quadrilateral is $360^o$ .

$\implies$ $\angle A + \angle B + \angle C + \angle D = 360^{o}$ .

Then, $\angle D$ will be given by:

$\angle D = 360^o - \angle A - \angle B-\angle C$

$\Rightarrow \angle D = 360 ^o-120^o -73^o -80^o$

$\Rightarrow \angle D = 360 - 273^o$

$\Rightarrow \angle D = 87^o$ .

The measure of fourth angle is $87 ^{o}$ .

Therefore, option $A$ is correct.

A quadrilateral can be drawn, if the measures of its

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four sides are given
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three sides and a diagonal are given
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four sides and one angle are given
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four angles and one side are given

Find the value of

$x + y + z + w$

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$180^o$
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$360^o$
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$240^o$
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none of the above

Explanation

Fourth angle of quadrilateral =

$360^o - (60^o + 80^o + 120^o)= 100^o$
Angle x =

$180^o - 120^o = 60^o$
Angle y =

$180^o - 80^o = 100^o$
Angle z =

$180^o - 60^o = 120^o$
Angle w =

$180^o - 100^o = 80^o$
x+y+z+w =

$60^o + 100^o + 120^o + 80^o = 360^o$

In the figure, PQRS is a parallelogram. If

$\angle P=75^o$ , then

$\angle Q=$

0%
$75^o$
0%
$90^o$
0%
$105^o$
0%
$100^o$

Explanation

In a

$\parallel gm$ sum of adjacent angles

$=180^{\circ}$

$\angle P+\angle Q=180^{\circ}\Rightarrow 75^{\circ}+\angle Q=180^{\circ}$

$\angle Q=105^{\circ}$

Find the angle measure

$x$ in the following figures

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$140^o$
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$120^o$
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$180^o$
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$220^o$

The angles of a quadrilateral are

$\displaystyle x^{\circ},\left ( x+5 \right )^{\circ},\left ( x+10 \right )^{\circ}\: and\: \left ( x+25 \right )^{\circ}$ then value of x is

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$\displaystyle 50^{\circ}$
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$\displaystyle 80^{\circ}$
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$\displaystyle 60^{\circ}$
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$\displaystyle 70^{\circ}$

Explanation

We have,

$\displaystyle x^{\circ}+\left ( x+5 \right )^{\circ}+\left ( x+10 \right )^{\circ}+\left ( x+25 \right )^{\circ}=360^{\circ}$

$\displaystyle 4x+40^{\circ}=360^{\circ}$

$\displaystyle 4x=320^{\circ}$

$\displaystyle x=80^{\circ}.$

If the diagonals of a quadrilateral are perpendicular bisectors of each other, it is always a________

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Rectangle
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Rhombus
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pentagon
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Parallelogram

Explanation

The diagonals of a Rhombus and Square bisect each other perpendicularly, so the quadrilateral should be

a Rhombus or a square, But for a quadrilateral to be a square, each angel in it should be

$90^{0}$ , which is not given,

Also square is not given in the options, so the correct option is Rhombus.

Can the angles

$110^o, 80^o, 90^o$ &

$105^o$ be the angles of quadrilateral?

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Yes
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No
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Cannot predict
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None of the above

Explanation

We know, by angle sum property, the sum of angles of a quadrilateral is $360^o$ .

Here, the sum of angle will be $= 110^o + 80^o + 90^o + 105^o = 385^o > 360^o$ .

Hence, the given angles cannot be the angles of a quadrilateral.

$\therefore$ The answer is No.

That is, option

$B$ is correct.

State whether the following statements are true or false
A rhombus is a regular quadrilateral.

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True
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False

State whether the following statements are true or false
Every parallelogram is a rhombus

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True
0%
False

Find the unknown angle in the figure.

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$40^{0}$
0%
$50^{0}$
0%
$60^{0}$
0%
$70^{0}$

Explanation

We know, by angle sum property, the sum of angles of a quadrilateral is $360^o$ .

The given angles are $50^o,130^o,120^o,x$ .
Then, $50^o+130^o+120^o+x=360^o$ .

Therefore, the unknown angle is:

$\Rightarrow$ $360^o - (50^o + 130^o + 120^o ) =x^{\circ}$

$\Rightarrow$ $x^o=360^o - 300^o =60^{\circ}$ .

Therefore, the unknown angle is $x^o=60^o$ .

Hence, option $C$ is correct.

State true or false:

Rhombus and square are quadrilaterals that have four sides of equal length.

0%
True
0%
False

Explanation

We know that, a square is a quadrilateral having all sides equal and all angles equal to

$90^o$ .

Also, a rhombus is a quadrilateral having all sides equal and opposite angles equal.

Hence, both rhombus and square are quadrilaterals that have four sides of equal length.

Hence, the given statement is true.

Can all the angles of a quadrilateral be right angles?

0%
Yes
0%
No
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Maybe
0%
Cannot be determined

Explanation

Let us take a quadrilateral

$ABCD$ with

$AC$ as its diagonal.

$\Delta ADC$ we have,

$\angle ACD+\angle CDA+\angle DAC={ 180 }^{ O }$ ........

$(i)$ [sum of the angles of a

$\Delta ={ 180 }^{ O }]$

Also, in

$\Delta ABC$ we have

$\angle ACB+\angle CBA+\angle BAC={ 180 }^{ O }$ ........

$(ii)$ [sum of the angles of a \Delta ={ 180 }^{ O }]$$ .

Adding

$(i)$ &

$(ii)$ , we have,

$\angle ACD+\angle CDA+\angle DAC+\angle ACB+\angle CBA+\angle BAC={ 360 }^{ O }$

$\Longrightarrow \angle A+\angle B+\angle C+\angle D={ 360 }^{ O }$

So, the sum of the angles of a quadrilateral is

${ 360 }^{ O }$ .......

$(iii)$ .

Now, if each angle is

${ 90 }^{ o }$ , then

$\angle A+\angle B+\angle C+\angle D={ 90 }^{ O }\times 4={ 360 }^{ O }$ .

It complies with

$(iii)$ .

Hence, all the angles of a quadrilateral can be right angles.

That is, the statement is true.

Therefore, option

$A$ is correct.

Name the quadrilaterals whose diagonals are perpendicular bisectors of each other

Answer: Rhombus; square

0%
True
0%
False

Explanation

A square is a 4 sided figure whose diagonals bisect each other at right angles.

A rhombus is a proper subset of a square.

It becomes a square when its every angle is a right angle.

$\therefore$ Diagonals of a rhombus bisect each other at right angles.

Ans- square, rhombus.

CBSE Questions for Class 9 Maths Quadrilaterals Quiz 1 - MCQExams.com

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Practice Class 9 Maths Quiz Questions and Answers

CBSE Questions for Class 9 Maths Quadrilaterals Quiz 1 - MCQExams.com

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Practice Class 9 Maths Quiz Questions and Answers

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