Match the following. $$(1)$$ Rectangle (p) A quadrilateral having its opposite sides equal and parallel. $$(2)$$ Square (q) A parallelogram having its opposite sides equal and each of the angle is a right angle. $$(3)$$ Parallelogram (r) A parallelogram having all sides equal and each of the angle is a right angle. $$(4)$$ Rhombus (s) A quadrilateral in which a pair of opposite sides are parallel. $$(5)$$ Trapezium (t) A parallelogram having all sides equal.

$$1\rightarrow (q), 2\rightarrow (r), 3\rightarrow (p), 4\rightarrow (t), 5\rightarrow (s)$$

$$1\rightarrow (t), 2\rightarrow (s), 3\rightarrow (r), 4\rightarrow (p), 5\rightarrow (q)$$

$$1\rightarrow (p), 2\rightarrow (q), 3\rightarrow (r), 4\rightarrow (s), 5\rightarrow (t)$$

$$1\rightarrow (r), 2\rightarrow (q), 3\rightarrow (t), 4\rightarrow (p), 5\rightarrow (s)$$

MCQ Questions for Class 9 Maths Quadrilaterals Quiz 2

Angles of a quadrilateral are in the ratio 3 : 6 : 8 :The largest angle is :

0%
$178^{\circ}$
0%
$90^{\circ}$
0%
$156^{\circ}$
0%
$36^{\circ}$

Explanation

Given ratio of angles are

$3 : 6 : 8 : 13$ .

Let the angles be

$3x$ ,

$6x$ ,

$8x$ ,

$13x$ .

By angle sum property, the sum of all angles of quadrilateral is

$360^o.$

So,

$3x+6x+8x+13x=360^o$

$\implies$

$30x=360^o$

$\implies$

$x=\dfrac{360^o}{30}$

$\implies$

$x=12^o$ .

Then,

$3x=3\times12^o=36^o$ ,

$6x=6\times12^o=72^o$ ,

$8x=8\times12^o=96^o$

and

$13x=13\times12^o=156^o$ .

Hence, the largest angle is

$156^o$ .

Therefore, option

$C$ is correct.

State whether true or false:

Name of some of the quadrilaterals whose diagonals bisect each other is parallelogram, rhombus, square, and rectangle.

0%
True
0%
False

Explanation

A parallelogram is a

$4$ sided figure whose diagonals bisect each other.

The set of a square, a rhombus, and a rectangle is a proper subset of the parallelogram.

Those figures contain all the properties of the parallelogram.

So diagonals of square, rhombus, and rectangle bisect each other as well.

Name the quadrilaterals whose diagonals are equal.
Answer: Square; rectangle

0%
True
0%
False

Explanation

A rectangle is a quadrilateral with opposite sides equal & parallel to each other.

Each angle is a right one.

In the figure, ABCD is a rectangle whose diagonals divide it into 4

$\Delta s$ viz.

$\Delta ABC$ ,

$\Delta ADC$ ,

$\Delta ABD$ &

$\Delta CBD$

Since all the angles are right ones, the above

$\Delta s$ are right

$\Delta s.$

So,

${ AC }^{ 2 }={ AB }^{ 2 }+{ BC }^{ 2 }$ &

${ BD }^{ 2 }={ CD }^{ 2 }+{ BC }^{ 2 }$

But

$AB=CD$ ...(opposite sides of a rectangle)

$\Longrightarrow { AC }^{ 2 }={ BD }^{ 2 }$

$\Longrightarrow AC=BD.$

So, the diagonals of a rectangle are equal.

Again a square is a special rectangle whose all sides are equal to each other.

$\therefore$ The diagonals of a square are equal.

Which of the following pair of shapes when joined together (by placing from edge to edge) can form a rectangle?

0%
0%
0%
0%
None of these

Explanation

Properties of rectangle are :

$\Rightarrow$ Each of the interior angles is 90

$^\circ$ .

$\Rightarrow$ Opposite sides of rectangle are parallel.

$\Rightarrow$ Opposite sides of rectangle are equal.

$\Rightarrow$ So, by joining pair of shapes of option B and C we will not form rectangle because they are not satisfying all the properties of rectangle.

$\Rightarrow$ So, only joining pair of shapes of option A, can form a rectangle because it's satisfy all the properties of rectangle.

Each angle of a square is of measure ___ .

0%
$\displaystyle 30^{\circ}$
0%
$\displaystyle 45^{\circ}$
0%
$\displaystyle 60^{\circ}$
0%
$\displaystyle 90^{\circ}$

Explanation

Each angle of a square is of measure

${90}^{o}$

Diagonals of a quadrilateral

$ABCD$ bisect each other. If

$\angle A=45^{\circ},$ then

$\angle B$ equals

0%
$45^{\circ}$
0%
$55^{\circ}$
0%
$135^{\circ}$
0%
$115^{\circ}$

Explanation

The diagonal bisect each other. By parallelogram theorem, if the diagonals of a quadrilateral bisect each other, then it is a parallelogram.
Hence, ABCD is a parallelogram.
In a parallelogram, sum of adjacent angles is 180

$\angle A + \angle B = 180$

$\angle B = 180 - 45$

$\angle B = 135^{\circ}$

The sum of all angles in a quadrilateral is equal to _____ right angles.

0%
$2$
0%
$3$
0%
$4$
0%
$360$

Explanation

Consider a quadrilateral

$ABCD$ .

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

To prove this, we join $A$ and $C$ , i.e. we draw the diagonal $AC$ .

In $\triangle ABC$ ,

$\angle CAB+\angle ABC+\angle BCA=180^{\circ}$ [Sum of all angles of a triangle is $180^{\circ}$ ]..... $(1)$ .

In $\triangle ACD$ ,

$\angle CAD+\angle ADC+\angle DCA=180^{\circ}$ [Sum of all angle of a triangle is $180^{\circ}$ ].... $(2)$ .

Adding $(1)$ and $(2)$ , we get,

$\left(\angle CAB+\angle ABC+\angle BCA \right)+ \left(\angle CAD+\angle ADC+\angle DCA \right)=180^{\circ}+180^{\circ}$

$\implies$ $\angle ABC+\angle ADC+(CAB+CAD)+(BCA+DCA)=360^{\circ}$

$\implies$ $\angle ABC+\angle ADC+\angle BAD+\angle BCD=360^{\circ}$

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

That is, the sum of all angles of a quadrilateral is $360^o=4\times90^o$ , i.e. $4$ right angles.

Therefore, option

$C$ is correct.

1964123_378460_ans_1f280963b0b4436e95b2a88153a28035.png

A parallelogram with equal angles is called a ..............................

0%
triangle
0%
kite
0%
rectangle
0%
rhombus

Explanation

$Rectangle$ is the only parallelogram which like a parallelogram has opposite sides parallel and all angles

$equal$ .
Therefore, C is the correct answer.

A Rhombus also satisfies the properties of a:

0%
Square
0%
Parallelogram
0%
Trapezium
0%
None of these

Explanation

A rhombus is a parallelogram. The definition of a parallelogram is a quadrilateral that has

$2$ pairs of parallel lines.

A parallelogram has properties including

$2$ pairs of congruent sides,

$2$ pairs of congruent opposite angles, supplementary consecutive angles, and diagonals that bisect each other.

A rhombus has all of these properties.

Which of the following statement(s) is/are false?

0%
Each diagonal of a quadrilateral divides it into two triangles
0%
Each side of a quadrilateral is less than the sum of the remaining three sides
0%
A quadrilateral can atmost have three obtuse angles
0%
A quadrilateral has four diagonals

If the diagonals of a quadrilateral bisect one another at right angles, then the quadrilateral is a:

0%
rhombus
0%
trapezium
0%
rectangle
0%
parallelogram

Explanation

If the diagonals of a quadrilateral bisect one another at right angles then the quadrilateral is a rhombus.
Also, if

$ABCD$ is a quadrilateral and diagonals

$AC$ and

$BD$ bisect each other at at right angles,

then in

$\triangle AOB$ &

$\triangle AOD$ ,

$DO=OB$ .....(

$O$ is mid point)

$AO=AO$ .....(COMMON SIDE)

$\angle AOB\quad =\angle AOD$ .....(Right angle)
Therefore,

$\triangle AOB \cong \triangle AOD$ ...(By

$RHS$ congruency criterion).

Then,

$AB=AD$ (By

$CPCT$ rule).

Similarly

$AB=BC=CD=AD$ can be proved which means that quadrilateral is a rhombus.

Hence, option

$A$ is correct.

A parallelogram is a quadrilateral whose ...................... sides are parallel.

0%
adjacent
0%
congruent
0%
opposite
0%
linear

Explanation

A parallelogram is a quadrilateral which has

$4$ sides whose opposite sides are equal and parallel. It has

$2$ pairs of parallel and equal sides.
Therefore, C is the correct answer.

If in a quadrilateral ABCD,

$\angle A = 120^o, \angle B = 60^o, \angle C = 100^o$ then

$\angle D =$ ...............

0%
80 $^o$
0%
90 $^o$
0%
180 $^o$
0%
360 $^o$

Explanation

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

$120^o + 60^o + 110^o + \angle D = 360^o$

$280^o + \angle D = 360^o$

$\angle D = 360^o - 280^o = 80^o$

In a quadrilateral

$ABCD$ ,

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

$\displaystyle \angle B + \angle D$ =

0%
$\displaystyle 360^{\circ}$
0%
$\displaystyle 100^{\circ}$
0%
$\displaystyle 180^{\circ}$
0%
$\displaystyle 80^{\circ}$

Explanation

We have

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

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

$\Rightarrow \displaystyle 180^{\circ}+ \left ( \angle B + \angle D \right )=360^{\circ}$

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

A parallelogram each of whose angle measures

$90^\circ$ is

0%
Rectangle
0%
Rhombus
0%
Triangle
0%
Trapezium

Explanation

In a parallelogram,

Both the pair of opposite sides are of equal length.

Opposite angles are equal and two adjacent angles are supplementary.

A rectangle is a parallelogram, in which each angle measures

$90^{o}$ .

Hence, a parallelogram each of whose angle measures

$90^{o}$ is a rectangle.

A quadrilateral whose all sides are equal and has four right angles is called a ____ .

0%
rectangle
0%
rhombus
0%
kite
0%
square

All parallelograms are quadrilaterals.

0%
True
0%
False

If in a quadrilateral the diagonals bisect each other, then it is a_____.

0%
rhombus
0%
parallelogram
0%
rectangle or square
0%
all of the above

Explanation

$\Rightarrow$ In rhombus opposite sides are parallel to each other and all sides are equal then, diagonals are bisect each other.

$\Rightarrow$ In parallelogram opposite sides are parallel to each other then diagonals are bisect each other.

$\Rightarrow$ And in rectangle and square also opposite sides are parallel and diagonals are bisect each other.

$\Rightarrow$ So, correct answer for these question is option D.

Refer to the figure above and calculate the value of

$x$ , if one angle is a right angle.

0%
$54$
0%
$56.25$
0%
$60$
0%
$67.5$
0%
$72$

Explanation

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

$\therefore 90^o+2x+x+x=360^o$

$\Rightarrow 4x=360^o-90^o$

$\Rightarrow 4x=270^o$

$\Rightarrow x=\dfrac{270^o}{4}=67.5^o$ .

Therefore, option

$D$ is correct.

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

0%
Rectangle
0%
Trapezium
0%
Rhombus
0%
Parallelogram

Explanation

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.

All the angles of a quadrilateral can be ___________.

0%
right angles
0%
acute angles
0%
obtuse angles
0%
Can't say

Explanation

We know, by angle sum property, the sum of all angles of quadrilateral

$= 360^o$ .

Then,
Sum of

$4$ right angles

$= (90˚ + 90˚ + 90˚ + 90˚)$

$= 360˚$ .

Sum of

$4$ acute angles

$= (<90˚ + <90˚ + <90˚ + <90˚)$

$< 360˚$ .

Sum of

$4$ obtuse angles

$= (>90˚ + >90˚ + >90˚ + >90˚)$

$>360˚$ .

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

Therefore, option

$A$ is correct.

If the diagonals of a quadrilateral bisect each other at right angle, then it is a __________.

0%
Kite
0%
Parallelogram
0%
Rhombus
0%
Rectangle

Explanation

The diagonals of a Rhombus bisect each other at an angle of

$90^0$ i.e. right angle.

Choose the correct statement.

0%
The diagonals of a parallelogram are equal
0%
The diagonals of a rectangle are perpendicular to each other
0%
If the diagonals of a quadrilateral intersect at right angles, it is not necessarily a rhombus
0%
Every quadrilateral is either a trapezium or a parallelogram or a kite

Explanation

$\textbf{Step-1: Analyze the options}$

$\text{Option A: The diagonals of a parallelogram are not equal.}$

$\text{Option B: The diagonals of a rectangle are not perpendicular to each other.}$

$\text{Option C: The diagonals of a square, rhombus, kite bisect each other at right angles,}$

$\text{not strictly for rhombus only.}$

$\text{Option D : There exist many quadrilaterals- square, rectangle, rhombus}$

$\textbf{Step-2: Conclusion}$

$\text{So, we can say that only one of the given options, (C) is correct.}$

$\text{We can say that if diagonals of a rhombus bisect each other, it is not necessarily a rhombus.}$

$\textbf{Thus, the correct option is C.}$

Match the following.

$(1)$ Rectangle	(p) A quadrilateral having its opposite sides equal and parallel.
$(2)$ Square	(q) A parallelogram having its opposite sides equal and each of the angle is a right angle.
$(3)$ Parallelogram	(r) A parallelogram having all sides equal and each of the angle is a right angle.
$(4)$ Rhombus	(s) A quadrilateral in which a pair of opposite sides are parallel.
$(5)$ Trapezium	(t) A parallelogram having all sides equal.

0%
$1\rightarrow (t), 2\rightarrow (s), 3\rightarrow (r), 4\rightarrow (p), 5\rightarrow (q)$
0%
$1\rightarrow (p), 2\rightarrow (q), 3\rightarrow (r), 4\rightarrow (s), 5\rightarrow (t)$
0%
$1\rightarrow (r), 2\rightarrow (q), 3\rightarrow (t), 4\rightarrow (p), 5\rightarrow (s)$
0%
$1\rightarrow (q), 2\rightarrow (r), 3\rightarrow (p), 4\rightarrow (t), 5\rightarrow (s)$

Explanation

1. Rectangle is a parallelogram with opposite sides equal and all sides at right angle to each other. Hence (q) is correct.

2. Square is a parallelogram with all sides equal and all the sides at right angle to each other. Hence (r) is correct.

3. Parallelogram is a quadrilateral which has equal opposite sides and both pair of opposite sides are parallel to each other. Hence (p) is correct.

4. Rhombus has all sides equal to each other but angle between sides isn't

$90^{\circ}$ and opposite angles are equal. Hence (t) is correct.

5. Trapezium is a quadrilateral with only one pair of opposite sides parallel to each other. Hence (s) is correct.

All kites are rhombuses.

0%
True
0%
False

Explanation

$\Rightarrow$ A rhombus is a quadrilateral with all sides of equal length.

$\Rightarrow$ A kite is a quadrilateral with two adjacent pairs of sides of equal length.

$\Rightarrow$ So, a kite does not have all sides equal in length. So kite cannot be a rhombus.

$\therefore$ All kites are rhombuses is a false statement.

1264267_703198_ans_26cc3877c12343528fc0430461656db7.jpeg

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

0%
Kite
0%
Trapezium
0%
Parallelogram
0%
None of these

State whether the statement is true/false.

In a parallelogram sum of any two consecutive angles is

$180^o$ .

0%
True
0%
False

Explanation

Since ABCD is a parallelogram. Therefore,

$AD \parallel BC$ .

Now,

$AD\parallel BC$ and transversal AB intersects them at A and B respectively.

Therefore,

$\angle A+\angle B=180^o$ [ interior angles ]

Similarly,

$\angle B+\angle C=180^o, \angle C+\angle D=180^o, \angle D+\angle A=180^o$ .

1334400_1112352_ans_60fd267c13ee4a09948132488b8e65da.png

Choose the correct alternative :
For every quadrilateral there are............element

0%
$4$
0%
$6$
0%
$10$
0%
$8$

The angle of a quadrilateral are in the ratio

$3 : 4 : 5 : 6$ . The largest of them is:

0%
${ 90 }^{ \circ }$
0%
${ 120 }^{ \circ }$
0%
${ 150 }^{ \circ }$
0%
${ 102 }^{ \circ }$

Explanation

Given the ratio of angles of quadrilateral, $ABCD$ is $3:4:5:6$ .

Let the angles of quadrilateral $ABCD$ be $3x,4x,5x,6x$ , respectively.

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

$\Rightarrow 3x+4x+5x+6x=360^\circ$

$\Rightarrow 18x=360^\circ$

$\therefore x=20^\circ$ .

$\angle A =3x$

$=3 \times 20^\circ$

$=60^\circ$

$\angle B =4x$

$=4\times 20^\circ$

$=80^\circ$

$\angle C =5x$

$=5 \times 20^\circ$

$=100^\circ$

$\angle D =6x$

$=6 \times 20^\circ$

$=120^\circ$

The largest angle is equal to $120^\circ.$ Hence, option $B$ is correct.

The sum of all the angles of a quadrilateral is:

0%
${ 180 }^{ \circ }$
0%
${ 270 }^{ \circ }$
0%
${ 360 }^{ \circ }$
0%
${ 400 }^{ \circ }$

Explanation

$\textbf{Step -1: Construction in the given quadrilateral.}$

$\text{Consider a quadrilateral }$

$ABCD$ .

$\text{Construct a line }AC \text{ i.e. the diagonal to quadrilateral }ABCD.$

$\textbf{Step -2: Sum of angles of a triangle.}$

$\text{We know, the sum of all angles of a triangle is }$

$180^{\circ}$

$\text{So, in }$

$\triangle ABC$ ,

$\angle CAB+\angle ABC+\angle BCA=180^{\circ}$

$...(i)$

$\text{And, in }$

$\triangle ACD$ ,

$\angle CAD+\angle ADC+\angle DCA=180^{\circ}$

$...(ii)$

$\textbf{Step -3: Adding above equations to get the sum of all the angles of a quadrilateral.}$

$\text{Adding (i) and (ii), we get, }$

$\left(\angle CAB+\angle ABC+\angle BCA \right)+ \left(\angle CAD+\angle ADC+\angle DCA \right)=180^{\circ}+180^{\circ}$

$\Rightarrow$

$\angle ABC+\angle ADC+(CAB+CAD)+(BCA+DCA)=360^{\circ}$

$\Rightarrow$

$\angle ABC+\angle ADC+\angle BAD+\angle BCD=360^{\circ}$

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

$\text{Hence, We can say that the sum of all the angles of a quadrilateral is }360^\circ$

$\textbf{Therefore, the sum of all the angles of a quadrilateral is }$

$\mathbf{360^\circ}$

CBSE Questions for Class 9 Maths Quadrilaterals Quiz 2 - MCQExams.com

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Practice Class 9 Maths Quiz Questions and Answers

CBSE Questions for Class 9 Maths Quadrilaterals Quiz 2 - MCQExams.com

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Practice Class 9 Maths Quiz Questions and Answers

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