MCQ Questions for Class 8 Maths Understanding Quadrilaterals Quiz 10

A diagonal of a paralleogram divides it into two congruent triangles.

0%
True
0%
False

Explanation

Let us consider a parallelogram

$ABCD$ with

$AC$ as its diagonal.

To prove:

$\triangle ABC \cong \triangle ADC$

Proof:

We know that the opposite sides of a parallelogram are parallel.

Hence

$AB \parallel DC$ and

$AD \parallel BC$

$AC$ is the transversal of the parallel lines

$AB$ and

$DC$

$\angle BAC =\angle DCA$ (Alternate angles)

$...(1)$

$AC$ is the transversal of the parallel lines

$AD$ and

$BC$

$\angle DAC =\angle BCA$

$...(2)$

$\triangle ABC$ and

$\triangle ADC,$

$\angle BAC =\angle DCA$

$AC$ is the common side

$\angle DAC =\angle BCA$

Therefore,

$\triangle ABC \cong \triangle ADC$

1465959_1303911_ans_680c786888b948c19ec04eb66a1745bb.png

State, with reason, whether the following statement is true or false:Every parallelogram is a rhombus.

0%
True
0%
False

If the quadrilateral

$ABCD$ is a parallelogram. What is the value of

$x$ ?

0%
$45^{\circ}$
0%
$30^{\circ}$
0%
$36^{\circ}$
0%
$37^{\circ}$

Explanation

In parallelogram

$ABCD,$

We know that the opposite angles of a parallelogram are equal.

Hence

$\angle A=\angle C$

$\Rightarrow 3{y} = 3x + {3}$

$...(1)$

and

$\angle B=\angle D$

$\therefore\ \angle D = 2y - {5}$

$...(2)$

We know that the sum of angles of a parallelogram is

$360^\circ$

$\Rightarrow (3y)+(3x+3)+(2y-{5})+(2y-{5})={360}$

$\Rightarrow 3y+3y+4y-10={360}$

$\Rightarrow 10y-{10}={360}$

$\Rightarrow 10y={360}+{10}$

$\Rightarrow 10y={370}$

$\Rightarrow y=\dfrac{370}{10} = {37^\circ}$

Substitute

$y=37^\circ$ in

$(1)$

$\Rightarrow 3\times {(37^\circ)} = 3x + {3^\circ}$

$\Rightarrow 111=3x+3$

$\Rightarrow 3x=111-3$

$\Rightarrow 3x=108$

$\Rightarrow x = \dfrac{{108}}{3} = 36^\circ$

In parallelogram

$ABCD$ , the bisectors of

$\angle A$ and

$\angle B$ intersect at

$M$ .If

$\angle A=80^{o}$ , then

$\angle AMB=$ .........

0%
$40^{o}$
0%
$50^{o}$
0%
$80^{o}$
0%
$90^{o}$

Explanation

Given in parallelogram

$ABCD, \; AM$ and

$BM$ are bisectors of

$\angle{A}$ and

$\angle{B}$ respectively.

As we know that sum of adjacent angles in a parallelogram is

$180°$ .

$\therefore \angle{A} + \angle{B} = 180°$

$\Rightarrow 2 \angle{BAM} + 2 \angle{ABM} = 180°$

$\Rightarrow \angle{BAM} + \angle{ABM} = \cfrac{180°}{2} = 90° ..... \left( 1 \right)$

Now, in

$\triangle{AMB}$ ,

$\angle{BAM} + \angle{AMB} + \angle{ABM} = 180°$

$\Rightarrow \angle{AMB} + 90° = 180°$

$\Rightarrow \angle{AMB} = 180° - 90° = 90°$

Measures of opposite angles of parallelogram are

$(3x-2) ^{\circ}$ and

$(50-x) ^{\circ}$ . Find the measure of its other angles.

0%
$143$
0%
$153$
0%
$163$
0%
$173$

Explanation

Here,

$ABCD$ is a parallelogram

Let

$\angle A=(3x-2)^o$ and

$C=(50-x)^o$

We know that in parallelogram opposite angles are equal.

$\therefore$

$\angle A=\angle C$

$\Rightarrow$

$3x-2=50-x$

$\Rightarrow$

$4x=52$

$\Rightarrow$

$x=13$

$\Rightarrow$

$\angle A=(3x-2)^o=(3\times 13-2)^o=37^o$

In parallelogram sum of adjacent angles are supplementary.

$\therefore$

$\angle A+\angle B=180^o$

$\Rightarrow$

$37^o+\angle B=180^o$

$\therefore$

$\angle B=143^o$

Hence other two equal opposite angles are

$143^o$

1256045_1378964_ans_5434876ffd9d44368c6ec9dcdf55592e.png

Diagonals of a parallelogram ABCD intersect at point O. If

$\angle BOC = 90^\circ$ and

$\angle BDC = 50^\circ$ , then

$\angle OAB$ is :

0%
$90^\circ$
0%
$50^\circ$
0%
$40^\circ$
0%
$10^\circ$

A quadrilateral with two pairs of opposite sides parallel, is a :

0%
a rhombus
0%
a kite
0%
a trapeziun
0%
a parallellogram

What type of angle is formed at the point of intersection of the angle bisectors of two adjacent angle of a parallelogram?

0%
Acute angle
0%
Complementary angle
0%
Right angle
0%
Obtuse angle

Say True or False.
All the sides of a rhombus are of equal length.

0%
True
0%
False

Say True or False.
All the sides of a parallelogram are of equal length.

0%
True
0%
False

Explanation

In parallelogram,

Opposite sides are equal is length.

Therefore in parallelogram ABCD

$.AB=CD$

$.BC=AD$

$.But AB\neq BC\neq CD\neq AD$

1338501_1644524_ans_a37d21fb95714c2b93a765cf1c7acbd5.png

The diagonals do not necessarily intersect at right angles in a

0%
parallelogram
0%
rectangle
0%
rhombus
0%
kite

Two adjacent angles of a parallelogram are

$\left(2x+25\right)^{o}$ and

$\left(3x-5\right)^{o}.$ The value of

$x$ is

0%
$28$
0%
$32$
0%
$36$
0%
$42$

Explanation

We know that sum of adjucent angled of a parallelogram is

$180^o$

$(2x+25)^o+(3x-5)^o=180^o$

$5x+20=180^o$

$5x=180^o - 20^o$

$5x=160^o$

$x=160^o/5=32^o$

Which of the following is a property of a parallelogram ?

0%
Opposite sides are parallel.
0%
The diagonals bisect each other at right angles.
0%
The diagonals are perpendicular to each other.
0%
All angles are equal.

In a parallelogram PQRS , if

$\angle\, P = 60^{\circ}$ , then other three angles are:

0%
$45^{\circ} , 135^{\circ} , 120^{\circ}$
0%
$60^{\circ} , 120^{\circ} , 120^{\circ}$
0%
$60^{\circ} , 135^{\circ} , 135^{\circ}$
0%
$45^{\circ} , 135^{\circ} , 135^{\circ}$

Explanation

Given:

$\angle\, P = 60^{\circ}$

$\therefore \, \angle\, R = 60^{\circ}$

$\therefore$ opposite angles are equals

Similarly,

$\angle Q = \angle S$

Now,

$\angle P+\angle Q = 180^o$ {supplementary angles because these interior angles lie on the same side of the transversal}

Therefore,

$\angle\, Q = \angle S = 180^o - 60^{\circ}$

$\angle\, Q = \angle S = 120^o$

If two adjacent angles of a parallelogram are in the ratio

$2 : 3$ , then the measure of angles are:

0%
$72^{\circ} , 108^{\circ}$
0%
$36^{\circ} , 54^{\circ}$
0%
$80^{\circ} , 120^{\circ}$
0%
$96^{\circ} , 144^{\circ}$

Explanation

Let the angles be

$2x , 3x$

$2 x + 3 x = 180$

$\Rightarrow \, 5x = 180$

$\Rightarrow \, 5x = 180$
So , the angles are

$2 \times 36 = 72$

$3 \times 36 = 108$

The angle between the two altitudes of a parallelogram through the same vertex of an obtuse angle of the parallelogram is

$30^{\circ}$ . The measure of the obtuse angle is

0%
$100^{\circ}$
0%
$150^{\circ}$
0%
$105^{\circ}$
0%
$120^{\circ}$

Explanation

ABCD is a parallelogram.

From the question it is given that, ∠EBF =

$30^o$

Sum of interior angles of a quadrilateral =

$360^o$

Then, ∠EBF + ∠BED + ∠EDF + ∠DFB =

$360^o$

∠EDF =

$360^o – (90^o + 90^o + 30^o)$

∠EDF =

$150^o$ which is an obtuse angle.

2002223_1792027_ans_db394ed3f34a4e14b790bf8ff3b48d13.png

State whether the statements are true (T) or (F) false:
The sum of interior angles and the sum of exterior angles taken in an order are equal in case of quadrilateral only.

0%
True
0%
False

Explanation

Sum of Interior angles of Polygon

$= 180(n - 2)$
Sum of Exterior angles of Polygon

$= 360$

$n = 4$
Sum of Interior angles of Polygon

$= 180(4 - 2) = 360^{\circ}$
Sum of Exterior angles of Polygon

$= 360$

State whether the statements are true (T) or (F) false.
If diagonals of a quadrilateral bisect each other , it must be a parallelogram.

0%
True
0%
False

State whether the statements are true (T) or (F) false.
If opposite angles of a quadrilateral are equal , it must be a parallelogram.

0%
True
0%
False

Explanation

Let's assume

$\angle$ A =

$\alpha$ and

$\angle$ B =

$\beta$
We need to prove that

$\angle$ C =

$\alpha$ and

$\angle$ D =

$\beta$

$\alpha + \beta = 180^{\circ}$ (co-interior angles , AD || BC

$\angle$ C =

$\alpha$ (Co-interior angles , AB || DC )

$\angle$ D =

$\beta$ (co-interior angles , AB || DC ).

1685045_1792500_ans_036be4b0fd7346149cbeeb79fa8b7705.png

All parallelograms having equal areas have same perimeters.

0%
True
0%
False

Boundaries of surfaces are:

0%
surfaces
0%
curves
0%
lines
0%
points

The sum of interior angles of a hexagon is:

0%
$720^{\circ}$
0%
$360^{\circ}$
0%
$540^{\circ}$
0%
$1080^{\circ}$

Explanation

$n$ -sided polygon,
sum of interior angles

$=(n-2)\times180^\circ$

Hexagon has 6 side

$n=6$

sum of interior angles of a hexagon

$=(6-2)\times180^\circ= 720^{\circ}$

If the two adjacent angles of a parallelogram are

$(3x-20^\circ)$ and

$(50^\circ -x)$ , then the value of

$x$ is:

0%
$55^\circ$
0%
$75^\circ$
0%
$20^\circ$
0%
$80^\circ$

Explanation

We know that sum of adjacent angles of a parallelogram is

$180^o$ .

Therefore,

$(3x-20^o)+(50^o-x)=180^o$

$2x+30^o=180^o$

$2x=150^o$

$x=75^o$

Option B is correct.

1977285_1879695_ans_fa71860f0aeb42d1896cf8a3371aacc2.jpg

Select which curves are open.

In a parallelogram

$ABCD$ , if

$AB = 2x + 5, CD = y + 1, AD = y + 5$ and

$BC = 3x - 4$ , what is the ratio of

$AB$ and

$BC$ ?

0%
$71 : 21$
0%
$12 : 11$
0%
$31 : 35$
0%
$4 : 7$

Explanation

In parallelogram, opposite sides are parallel and equal

$\therefore AB=CD$ and

$AD=BC$

$\Rightarrow 2x+5=y+1\longrightarrow 1$

$\Rightarrow 3x-4=y+5\longrightarrow 2$
Equation 2-equation 1

$\left( 3x-2x \right) -4-5=0+4$

$x=13$
Put value of x in 1

$2(13)+5-1=y$

$y=30$

$\cfrac { AB }{ BC } =\cfrac { 2x+5 }{ 3x-4 } =\cfrac { 2(13)+5 }{ 3(13)-4 }$

$\cfrac { AB }{ BC } =\cfrac { 31 }{ 35 }$

$\therefore AB:BC=31:35$

If an angle of a parallelogram is four-fifths of its adjacent angle, what are the angles of the parallelogram?

0%
$60^o, 120^o, 60^o, 120^o$
0%
$90^o, 90^o,90^o,90^o$
0%
$80^o, 100^o,80^o,100^o$
0%
$30^o, 150^o, 30^o, 150^o$

In the diagram, KLMN is a constructed parallelogram.
Find the value of

$\angle KLM$

0%
$15^0$
0%
$30^0$
0%
$45^0$
0%
$60^0$

The parallelogram PQRS is formed by joining together four equilateral triangles of side 1 unit, as shown in the figure.
What is the length of the diagonal SQ?

0%
$\sqrt{7}$
0%
$\sqrt{8}$
0%
$\sqrt{6}$
0%
$\sqrt{5}$

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

0%
A parallelogram in which two adjacent angles are equal is a rectangle.
0%
A quadrilateral in which both pairs of opposite angles are equal is parallelogram
0%
In a parallelogram the number of acute angles is two.
0%
All of these

If ABCD is a parallelogram, then

$\angle A - \angle C = \underline{ }$

0%
$180^0$
0%
$0^0$
0%
between $10^0$ & $180^0$
0%
None of these

CBSE Questions for Class 8 Maths Understanding Quadrilaterals Quiz 10 - MCQExams.com

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Practice Class 8 Maths Quiz Questions and Answers

CBSE Questions for Class 8 Maths Understanding Quadrilaterals Quiz 10 - MCQExams.com

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Practice Class 8 Maths Quiz Questions and Answers

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