NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals

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# NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals

Edited By Ramraj Saini | Updated on Oct 09, 2023 02:29 PM IST

## NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals

Understanding Quadrilaterals Class 8 Questions And Answers provided here. These NCERT Solutions are created by expert team at craeers360 keeping the latest syllabus and pattern of CBSE 2023-23. A geometrical closed shape made by using 4 straight lines and having four connecting points is called Quadrilateral. The sum of the interior angles in a quadrilateral is always 360 degrees. NCERT Solutions for Class 8 Maths chapter 3 Understanding Quadrilaterals are covering the chapter to help you with the answers and conceptual clarity. It carries around 35% of geometry weightage and includes most important types of questions based on concepts of rectangles, squares, rhombus, parallelograms, trapezium, etc.

NCERT solutions for Class 8 Maths discussed all questions and answers of all chapters including chapter 3 understanding quadrilaterals. The subtopics covered under the chapter are polygons, angle sum property, properties of different kinds of quadrilaterals. In this particular chapter, there are 4 exercises consisting of a total of 31 questions. NCERT solutions for Class 8 Maths chapter 3 Understanding Quadrilaterals is covering every question in a comprehensive manner.

## Understanding Quadrilaterals Class 8 Solutions - Important Formulae

Polygons are categorised based on the quantity of sides or vertices they possess, as outlined below:

• Angle Sum Property for Quadrilaterals: The sum of all angles of a quadrilateral is 360°.

• Sum of the Measures of Exterior Angles of a Polygon: Regardless of the number of sides in a polygon, the total measure of the exterior angles equals 360 degrees.

>> Categories of Quadrilaterals: Quadrilaterals are grouped based on the measurements of their angles and side lengths. The area represents the total space enclosed by the figure, while the perimeter is the complete distance around its boundaries. Here, you'll find descriptions, area calculations, and perimeter formulas for different types of quadrilaterals:

## Understanding Quadrilaterals Class 8 NCERT Solutions (Intext Questions and Exercise)

NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Exercise: Angle Sum Property

As shown in $\triangle$ ACD,

$\angle 1 + \angle 2+\angle 3 = 180\degree$

As shown in $\triangle$ ABC,

$\angle 4 + \angle 5+\angle 6 = 180\degree$

$\angle A + \angle B +\angle C + \angle D= (\angle 1+\angle 4) +\angle 6 + (\angle 2+\angle 5) + \angle 3$ ( Since, $\angle A = (\angle 1+\angle 4)$ , $\angle B = \angle 6$ , $\angle C = (\angle 2+\angle 5)$ ,

$\angle D = \angle 3$ )

$\angle A + \angle B +\angle C + \angle D= (\angle 1+\angle 2 +\angle 3) + (\angle 4+\angle 5 + \angle 6)$

$= 180\degree + 180\degree$

$= 360\degree$

Hence proved, the sum of the measures of $\angle A,\angle B,\angle C$ and
$\angle D$ amounts to $180\degree + 180\degree = 360\degree$ .

What can you say about the sum of the angles ∠1, ∠2, ∠3 and ∠4?

[Note: We denote the angles by ∠1, ∠2, ∠3, etc., and their respective measures by m∠1, m∠2, m∠3, etc.]

The sum of the measures of the four angles of a quadrilateral is___________.
You may arrive at this result in several other ways also.

As we know the sum of all four angles of a quadrilateral is $360\degree$ .

$\angle 1,\angle 2,\angle 3,\angle 4$ are four angles of quadrilateral ABCD.

Hence, the sum of these angles is $360\degree$ = $\angle 1+\angle 2+\angle 3+\angle 4$

Angles ∠1, ∠2, ∠3, ∠4 meet at a point and sum of these angles is $360\degree$ = $\angle 1+\angle 2+\angle 3+\angle 4$ .

Draw a line matching points B and D.Line BD divides ABCD in two triangles . $\triangle BCD$ and $\triangle ABD$ .

Sum of angles of $\triangle BCD$ = $\angle DBC + \angle BDC + \angle C = 180\degree$ $\cdot \cdot \cdot \cdot \cdot \cdot \cdot \left ( 1 \right )$

Sum of angles of $\triangle ABD$ = $\angle ADB + \angle ABD + \angle A = 180\degree$ $\cdot \cdot \cdot \cdot \cdot \cdot \cdot \left ( 2\right )$

Here, $\angle ADB + \angle BDC = \angle D$

$\angle DBC + \angle ABD = \angle B$

Adding equation 1 and equation 2,

$(\angle DBC + \angle BDC + \angle C ) +$ $(\angle ADB + \angle ABD + \angle A )$ $=$ $360\degree$ { $\angle ADB + \angle BDC = \angle D$ and

i.e. $\angle A + \angle B +\angle C +\angle D$ = $360\degree$ . $\angle DBC + \angle ABD = \angle B$ }

The sum of the interior angles in a quadilateral,

$\angle A + \angle B +\angle C +\angle D$ = $360\degree$

NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals - Exercise: 3.1

Classify each of them on the basis of the following.

(a) Simple curve

(a) Simple curve : The curve which does not cross itself and have only one curve.

Some simple curves are $: 1,2,5,6,7$

Classify each of them on the basis of the following.

(b) Simple closed curve

Simple closed curve : The simple curves which are closed by line segment or curved line.

Some simple closed curve are $:1,2,5,6,7$

Classify each of them on the basis of the following.

(c) Polygon

A normally closed curve made up of more than 4 line segments is called a polygon.

Some polygons are shown in figures $1,2.$

Classify each of them on the basis of the following.

(d) Convex polygon

(d) Convex polygon :Convex polygon are polygons having all interior angles less than $180\degree$ .

Convex polygon = 2.

Classify each of them on the basis of the following.

(e) Concave polygon

(e) Concave polygon : Concave polygon have one or more interior angles greater than $180\degree$ .

Concave polygon = 1.

Q2 (a) How many diagonals does each of the following have?

There are 2 diagonals in a convex quadrilateral.

A regular hexagon

(b) A regular hexagon :

Total number of diagonal a regular hexagon have are 9 .

A triangle

(c) A triangle

A triangle does not have any diagonal.

The sum of the measures of the angles of a convex quadrilateral is $360\degree$ . A convex quadrilateral is made of two triangles and sum of angles of a triangle is $180\degree$ . Hence,sum of angles of two triangles is $360\degree$ which is also sum of angles of a quadrilateral.

Here,as we can see this quadrilateral has two triangles and the sum of angles of these triangles is $180\degree+ 180\degree=360\degree$ = sum of all angles of a quadrilateral.

What can you say about the angle sum of a convex polygon with the number of sides?

(a) 7

(a) 7

the sum of angles of a convex polygon $= (number of sides - 2)\ast 180\degree$

the sum of angle of a convex polygon with 7 sides $= (7 - 2)\ast 180\degree$

the sum of angles of a convex polygon with 7 sides $= (5)\ast 180\degree$

the sum of angles of a convex polygon with 7 sides $= 900\degree$

What can you say about the angle sum of a convex polygon with the number of sides?

(b) 8

(b) 8

The sum of the angles of a convex polygon $= (number of sides - 2)\ast 180\degree$

The sum of the angles of a convex polygon with 8 sides $= (8 - 2)\ast 180\degree$

The sum of the angles of a convex polygon with 8 sides $= (6)\ast 180\degree$

The sum of the angles of a convex polygon with 8 sides $= 1080\degree$

What can you say about the angle sum of a convex polygon with number of sides?

(c) 10

(c) 10

angle sum of a convex polygon $= (number of sides - 2)\ast 180\degree$

angle sum of a convex polygon with 10 sides $= (10 - 2)\ast 180\degree$

angle sum of a convex polygon with 10 sides $= (8)\ast 180\degree$

angle sum of a convex polygon with 10 sides $= 1440\degree$

What can you say about the angle sum of a convex polygon with number of sides?

(d) $n$

(d) $n$

All the angles of a convex polygon added up to $= (number of sides - 2)\ast 180\degree$

the sum of the angles of a convex polygon having n sides $= (n - 2)\ast 180\degree$

A regular polygon is a polygon which has equal sides and equal angles.

The name of a regular polygon of 3 sides is an equilateral triangle.

All sides of the equilateral triangle are equal and angles are also equal.

Each angle = $60\degree$

A regular polygon is a polygon which has equal sides and equal angles.

The name of a regular polygon of 4 sides is square.

Square has all angles of $90\degree$ and all sides are equal.

A regular polygon is a polygon which have equal sides and equal angles.

The name of a regular polygon of 6 sides is a hexagon.

All angles of the hexagon are $120\degree$ each.

The solution for the above-written question is mentioned below,

Sum of angles of a quadrilateral $= 360\degree$

$130\degree+120\degree+50\degree+x= 360\degree$

$300\degree+x= 360\degree$

$x = 360\degree-300\degree$

$x = 60\degree$

The Solution for the above-written question is mentioned below,

Sum of angles of a quadrilateral $= 360\degree$

$90\degree+60\degree+70\degree + x=360\degree$

$220\degree + x=360\degree$

$x=360\degree-220\degree$

$x=140\degree$

This pentagon has all sides and all angles equal.

Sum of all angles of pentagon is $540\degree$

$x+x+x+x+x=540\degree$

$5\ast x=540\degree$

$x=108\degree$

$a+70\degree=180\degree$ (linear pair) $b+60\degree =180\degree$ (linear pair)

$a =110\degree$ $b =120\degree$

Sum of all angles of pentagon = $540\degree$

$110\degree+120\degree+x+x+30\degree=540\degree$

$260\degree+2x=540\degree$

$2x=540\degree-260\degree$

$2x=280\degree$

$x=140\degree$

(a) Find

$x + y + z$

$z+30\degree=180\degree$

$z=150\degree$

$x+90\degree=180\degree$

$x=90\degree$

The Sum of all angles of triangle is $180\degree$

the unmarked angle of triangle be A. $A+90\degree+30\degree=180\degree$

$A=180\degree-120\degree$

$A=60\degree$

$A+y=180\degree$

$60\degree+y=180\degree$

$y=180\degree - 60\degree$

$y=120\degree$

$x + y + z$ = $90\degree+120\degree+150\degree$

$x + y + z$ = $360\degree$

Here you will find the detailed solution of the above-written question,

$x+120\degree = 180\degree$

$x=180\degree - 120\degree$

$x=60\degree$

$y+80\degree = 180\degree$

$y=180\degree - 80\degree$

$y=100\degree$

$z+60\degree = 180\degree$

$z=180\degree - 60\degree$

$z=120\degree$

Sum of all angles of quadrilateral = $360\degree$

Let the unmarked angle be A.

$A+120\degree+60\degree+80\degree=360\degree$

$A=100\degree$

$A+w=180\degree$

$w= 80\degree$

$x + y + z + w$ = $60\degree+100\degree+120\degree+80\degree$

$x + y + z + w$ = $360\degree$

NCERT solutions for class 8 maths chapter 3 Understanding Quadrilaterals Excercise: Sum of the Measures of the Exterior Angles of a Polygon

Take a regular hexagon Fig 3.10.
Q1 What is the sum of the measures of its exterior angles $x, y, z, p, q, r$

the sum of all its exterior angles will be equal to $360\degree$ .

x,y,z,p,q,r are all exterior angles.

Hence, $x+y+z+p+q+r=360\degree$

It is a hexagon with all sides equal.

All interior angles are also equal.

$a+r=a+x=a+y=a+z=a+p=a+q=180\degree$ (linear pairs)

$r=x=y=z=p=q=180\degree - a$

Hence, $x = y = z = p = q = r$

because it is a hexagon with all sides and angles equal.

It is a hexagon with all sides equal.

All interior angles are also equal.

Sum of all angles of hexagon is $720\degree$ .

$6a = 720\degree$

$a = 120\degree$

$a+r=a+x=a+y=a+z=a+p=a+q=180\degree$ (linear pairs)

$r=x=y=z=p=q=180\degree - a$

Each exterior angle = $r=x=y=z=p=q=180\degree - a$ = $180\degree-120\degree$ = $60\degree$

It is a hexagon with all sides equal.

All interior angles are also equal.

Sum of all angles of the hexagon is $720\degree$ .

$6a = 720\degree$

$a = 120\degree$

(i) a regular octagon: It has all 8 angles equal and sum of all eight angles is 1080. Interior angles are equal so exterior angles are also equal.

Let interior angle be A.

$8\ast A= 1080\degree$

$A= 135\degree$ .

All exterior angles be B.

$B=180\degree - 135\degree$

$B=45\degree$

(ii) a regular 20-gon: It has all 20 angles equal and sum of all eight angles is 3240.Interior angles are equal so exterior angles are also equal.

Let interior angle be A.

$20\ast A= 3240\degree$

$A= 162\degree$ .

All exterior angles be B.

$B=180\degree - 162\degree$

$B=18\degree$

Class 8 maths chapter 3 question answer - Exercise: 3.2

Sum of all exterior angles of a polygon is $360\degree.$

$x+125\degree+125\degree=360\degree.$

$x=360\degree-250\degree.$

$x=110\degree.$

Sum of all exterior angles of polygon is $360\degree$

$x+90\degree+60\degree+90\degree+70\degree=360\degree$

$x=360\degree-310\degree$

$x=50\degree$

A regular polygon of 9 sides has all sides, interior angles and exterior angles equal.

Sum of exterior angles of a polygon = $360\degree$

Let the interior angle be A.

Sum of exterior angles of 9 sided polygon = $9 \ast A =$ $360\degree$

Exterior angles of 9 sided polygon $= A= 360\degree \div 9$

$A= 40\degree$

Hence, the measure of each exterior angle of a regular polygon of 9 sides is $40\degree$

A regular polygon of 15 sides has all sides, interior angles and exterior angles equal.

Sum of exterior angles of a polygon = $360\degree$

Let the interior angle be A.

Sum of exterior angles of 15 sided polygon = $15 \ast A =$ $360\degree$

Exterior angles of 15 sided polygon $= A= 360\degree \div 15$

$A= 24\degree$

Hence, the measure of each exterior angle of a regular polygon of 15 sides is $24\degree$

The measure of an exterior angle is 24°

A regular polygon has all exterior angles equal.

Sum of exterior angles of a polygon = $360\degree$

Let a number of sides be X.

Sum of exterior angles of a polygon = $X \ast 24\degree =$ $360\degree$

Exterior angles of 15 sided polygon $= X= 360\degree \div 24\degree$

$X= 15$

Hence, $15$ sided regular polygon have measure of an exterior angle 24°

The measure of each interior angle is 165°

So, measure of each exterior angle = 180°-165° = 15°

Regular polygon has all exterior angles equal.

Let number of sides of polygon = n

Sum of Exterior angles of a polygon = $360\degree$

$\left ( n \right )\ast 15\degree= 360\degree$

$n = 24$

Hence,regular polygon having each of its interior angles is 165° has 24 sides.

The measure of an exterior angle is 22°

A regular polygon has all exterior angles equal.

Sum of exterior angles of a polygon = $360\degree$

Let the number of sides be X.

Sum of exterior angles of a polygon = $X \ast 22\degree =$ $360\degree$

Exterior angles of 15 sided polygon $= X= 360\degree \div 22\degree$

$X= 16.36$

Hence, the side of a polygon should be an integer but as shown above, the side is not an integer. So,it is not possible to have a regular polygon with the measure of each exterior angle as 22o.

The measure of an interior angle is 22°

A regular polygon has all interior angles equal.

Let the number of sides and number of interior angles be n.

Sum of interior angles of a polygon = $\left ( n-2 \right )\ast 180\degree$

Sum of interior angles of a polygon = $\left ( n-2 \right )\ast 180\degree$ = $\left ( n \right )\ast 22\degree$

$\left ( n \right )\ast 180\degree-\left ( 2 \right )\ast 180\degree=\left ( n \right )\ast 22\degree$

$\left ( n \right )\ast 180\degree-\left ( n \right )\ast 22\degree= 360\degree$

$\left ( n \right )\ast 158\degree= 360\degree$

$n = 2.28$

The number of sides of a polygon should be an integer but since it is not an integer.So, it cannot be a regular polygon with interior angle as 22o

Q6 (a) What is the minimum interior angle possible for a regular polygon? Why?

Consider a polygon with the lowest number of sides i.e. 3.

Sum of interior angles of 3 sided polygon = $\left ( 3-2 \right )\ast 180\degree=180\degree$

Interior angles of a regular polygon are equal = A .

$\therefore$ $A+A+A=180\degree$

$3\ast A=180\degree$

$A=60\degree$

Hence,the minimum interior angle possible for a regular polygon is $60\degree$ .

Let there be a polygon with the minimum number of sides i.e. 3.

Exterior angles an equilateral triangle has a maximum measure.

Sum of exterior angles of polygon = $360\degree$

Let the exterior angle be A.

$\therefore$ $A+A+A=360\degree$

$3\ast A=360\degree$

$A=120\degree$

Hence, the maximum exterior angle possible for a regular polygon is $120\degree$ .

NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals - Topic: Kinds of Quadrilaterals

You get a trapezium. (Check it!) Which are the parallel sides here? Should the
non-parallel sides be equal?
You can get two more trapeziums using the same set of triangles. Find them out and
discuss their shapes.

AB and CD are parallel sides.BC and AD are nonparallel sides. Non-parallel sides need not be equal.

We can get two more trapeziums using the same set of triangles-

and

## NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals - Topic: Kite

Fold both the diagonals of the kite. Use the set-square to check if they cut at

right angles. Are the diagonals equal in length? Verify (by paper-folding or measurement) if the diagonals bisect each other. By folding an angle of the kite on its opposite, check for angles of equal measure.
Observe the diagonal folds; do they indicate any diagonal being an angle bisector? Share your findings with others and list them. A summary of these results are given elsewhere in the chapter for your reference. Show that triangle ABC and triangle ADC
are congruent. What do we infer from this?

Kite has symmetry along AC diagonal. and are congruent and equal triangles.

Diagonals AC and BD are of different lengths.

Diagonals bisect each other.

The two diagonals AC and BD bisect .

NCERT Solutions for Class 8 Maths 3 Understanding Quadrilaterals Excercise: Elements of Parallelogram

Here $\overline{AB}$ is same as $\overline{A'B'}$ except for the name. Similarly the other corresponding
sides are equal too.
Place $\overline{A'B'}$ over $\overline{DC}$ . Do they coincide? What can you now say about the lengths
$\overline{AB}$ and $\overline{DC}$ ?
Similarly examine the lengths $\overline{AD}$ and $\overline{BC}$ . What do you find?
You may also arrive at this result by measuring $\overline{AB}$ and $\overline{DC}$ .

Take cut-outs of two identical parallelograms, say ABCD and A′B′C′D′ (Fig 3.19).

Here $\overline{AB}$ is same as $\overline{A'B'}$ .

Also, $\overline{CD}$ is same as $\overline{C'D'}$

Place $\overline{A'B'}$ over $\overline{DC}$ . They coincide with each other.

The lengths $\overline{AB}$ and $\overline{DC}$ are equal and parallel lines.

The lengths $\overline{AD}$ and $\overline{BC}$ are equal and parallel lines.

Property : The opposite sides of a parallelogram are of equal length.

As we can see in the figure above, the opposite sides of figure are equal.

The figure above is a rectangle which is part of parallelogram.

Hence, the opposite sides of a parallelogram are of equal length.

As shown in the above figure opposites angles are equal and are equal to $90 \degree$ .

Hence,the figure obtained help you to confirm the property: The opposite angles of a parallelogram are of equal measure.

ABCD (Fig 3.29). Let its diagonals $\overline{AC}$ and $\overline{DB}$ meet at O.
Find the mid point of $\overline{AC}$ by a fold, placing C on A. Is the
mid-point same as O?
Does this show that diagonal $\overline{DB}$ bisects the diagonal $\overline{AC}$ at the point O? Discuss it
with your friends. Repeat the activity to find where the mid point of $\overline{DB}$ could lie.

ABCD . Let its diagonals $\overline{AC}$ and $\overline{DB}$ meet at O.
The mid point of $\overline{AC}$ is at point O.Hence, the
mid-point is same as O.

This show that diagonal $\overline{DB}$ bisects the diagonal $\overline{AC}$ at the point O.

The mid point of $\overline{DB}$ is point O.

Class 8 maths chapter 3 NCERT Solutions - exercise: 3.3

$AD =$ ......

In a parallelogram, opposite sides are equal in lengths.

Hence,

$AD = BC$

$\angle DCB =$ ......

In a parallelogram ,opposite angles are equal.

(ii) $\angle DCB =$ $\angle BAD.$

$OC =$ ......

In a parallelogram, both diagonals bisect each other.

$OC =$ $OA$

$m \angle DAB + m\angle CDA =$ .....

In a parallelogram, adjacent angles are supplementary to each other.

(iv) $m \angle DAB + m\angle CDA =$ $180\degree$

In a parallelogram, adjacent angles are supplementary to each other.

$\angle B+\angle C = 180\degree$

$100\degree+ x = 180\degree$

$x = 80\degree$

Opposite angles are equal.

Hence, z = $x = 80\degree$

and y = 100

$50\degree+x=180\degree$ ( Two adjacent angles are supplementary to each other)

$x=130\degree$

x=y= $130\degree$ (opposite angles are equal)

z=x= $130\degree$ ( corresponding angles are equal)

x= $90\degree$ (vertically opposite angles)

$x+y+30\degree = 180\degree$ (sum of angles of a triangle is $180\degree$ )

$90\degree+y+30\degree = 180\degree$

$y = 60\degree$

y=z= $60\degree$ (alternate interior angles)

$x+80\degree=180\degree$ (adjacent angles are supplementary)

$x=100\degree$

y = $80\degree$ ( opposite angles are equal)

z= $80\degree$ (corresponding angles are equal)

y = $112 \degree$ (opposite angles are equal)

$z+40\degree+112 \degree=180\degree$ (adjacent angles are supplementary)

$z=180\degree -152\degree$

$z=28\degree$

x = z = $28\degree$ (alternate angles are equal)

(i) $\angle D + \angle B = 180\degree$

Opposite angles should be equal and adjacent angles should be supplementary to each other.

$\angle B,\angle D$ are opposite angles.

Hence, a quadrilateral ABCD can be a parallelogram but it is not confirmed.

$AB = DC = 8 cm, AD = 4 cm$ and $BC = 4.4 cm$ ?

Opposite sides of a parallelogram are equal in length.

Since, $AD = 4 cm$ and $BC = 4.4 cm$ are opposite sides and have different lengths.

No, it is not a parallelogram.

Opposite angles of a parallelogram are equal

Since here $\angle A = 70 \degree$ and $\angle C = 65 \degree$ are different.

So, it is not a parallelogram.

The above-shown figure shows two opposite angles equal. $\angle B=\angle D$ .

But, it's not a parallelogram because the other two angles are different i.e. $\angle A\neq \angle C$ .

The measures of two adjacent angles of a parallelogram are in the ratio 3 : 2.

Sum of adjacent angles is $180\degree$ .

$\therefore$ $3\times x+2\times x = 180\degree$

$5\times x = 180\degree$

$x = 36\degree$

Hence, angles are $2\times 36\degree=72\degree$ and $3\times 36\degree=108\degree$ .

Let there be a parallelogram ABCD then, $\angle A=\angle C=108\degree$ and $\angle B=\angle D=72\degree$ . (Opposite angles are equal).

Given: Two adjacent angles of a parallelogram have equal measure = $\angle A= \angle B$ .

$\angle A+ \angle B =180\degree$ ( adjacent angles of a parallelogram are supplementary)

$2\times \angle A =180\degree$

$\angle A =90\degree$

$\therefore$ $\angle A=\angle B =90\degree$

$\angle A=\angle C =90\degree$ and $\angle B=\angle D =90\degree$ ( Opposite angles of a parallelogram are equal)

Hence, $\angle A=\angle B=\angle C=\angle D =90\degree$

The adjacent figure HOPE is a parallelogram.

$\angle HOP +70\degree = 180\degree$ (linear pairs)

$\angle HOP = 110\degree$

$x= \angle HOP = 110\degree$ (opposite angles of a parallelogram are equal)

$\angle HOP +\angle EHO = 180\degree$ ( adjacent angles are supplementary )

$110\degree +(40\degree+z) = 180\degree$

$z = 180\degree - 150\degree$

$z = 30\degree$

y= $40\degree$ (Alternate interior angles are equal)

GUNS is a parallelogram, so opposite sides are equal in length

$SG\:=\:UN$

$3\times x=18$

$x=18\div 3$

$x=6$

$UG\:=\:NS$

$3\times Y-1=26$

$3\times Y=27$

$Y=9$

Hence, $x=6$ cm and $Y=9$ cm.

Diagonals of a parallelogram intersect each other.

$y+7=20$

$y=20-7$

$y=13$

$x+y=16$

$x=16-13$

$x=3$

Hence, $x=3$ cm and $y=13$ cm.

$\angle SKR +\angle KSI = 180\degree$ ( adjacent angles are supplemantary)

$\angle KSI = 180\degree-120\degree$

$\angle KSI = 60\degree$

$\angle CLU=\angle UEC = 70\degree$ (oppsite angles are equal)

$x+ \angle UEC+\angle KSI = 180\degree$ (sum of angles of a triangle is $180\degree$ )

$x+ 70\degree+60\degree = 180\degree$

$x=180\degree -130\degree$

$x=50\degree$

Given, $\angle M+\angle L=100\degree+80\degree$ = $180\degree$ .

A transverse line is intersecting two lines such that the sum of angles on the same side of the transversal line is $180\degree$ .

And hence, lines KL and MN are parallel to each other.

Quadrilateral KLMN has a pair of parallel lines so it is a trapezium.

Given , $\overline{AB} || \overline{DC}$

$\angle B+\angle C=180\degree$ (Angles on same side of transversal)

$120\degree+\angle C=180\degree$

$\angle C=180\degree - 120\degree$

$\angle C=60\degree$

Hence, $m\angle C=60\degree$ .

Given, $\overline {SP} || \overline {RQ}$

$\angle P+\angle Q=180\degree$ (angles on the same side of transversal)

$\angle P=180\degree-130\degree$

$\angle P=50\degree$

$\angle R+\angle S=180\degree$ (angles on the same side of transversal)

$\angle S=180\degree-90\degree$

$\angle S=90\degree$

Yes, to find $m\angle P$ there is more than one method.

PQRS is quadrilateral so the sum of all angles is 360

$\angle P+\angle Q+\angle R+\angle S=360\degree$

and we know $\angle Q,\:\angle R ,\:\angle S$

so put values of $\angle Q,\:\angle R ,\:\angle S$ and we get a measurement of $\angle P$

NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals - Topic: Squares

PO = OR ( Square is a type of parallelogram)

By SSS congruency rule, $\triangle POS$ and $\triangle ROS$ are congruent triangles.

$\triangle POS\cong \triangle ROS$

$\therefore \angle POS = \angle ROS$

& $\angle POS + \angle ROS = 180\degree$

$2\times \angle ROS = 180\degree$

$\angle ROS = 90\degree$

Hence, $\angle O = 90\degree$ .

Thus,we can say that the diagonals of a square are perpendicular bisectors of each other

NCERT Solutions for Class 8 Maths 3 Understanding Quadrilaterals Exercise: 3.4

(a). False, All squares are rectangles but all rectangles cannot be square.

True. The opposite sides of the rhombus are parallel and equal.

True. All squares are rhombus because rhombus has opposite sides parallel and equal and same square has.

Also, all squares are rectangles because they have all interior angles as $90\degree$ .

False.

All squares have their opposite sides equal and parallel. Hence, they are parallelograms.

False,

Kites do not have all sides equal so they are not rhombus.

True, all rhombuses are kites because they have two adjacent sides equal.

True, all parallelograms are trapezium because they have a pair of parallel sides.

True, All squares are trapeziums because all squares have pairs of parallel sides.

The quadrilateral having four sides of equal length are square and rhombus.

All the quadrilaterals that have four right angles are rectangle and square

A square is a quadrilateral because a square has four sides.

A square is a parallelogram because the square has opposite sides parallel to each other.

A square is a rhombus because a square has four sides equal.

A square is a rectangle since it has all interior angles of $90\degree$ .

The quadrilaterals whose diagonals bisect each other are square, rectangle, parallelogram and rhombus.

The quadrilaterals whose diagonals are perpendicular bisectors of each other are rhombus and square.

The quadrilaterals whose diagonals are equal are squares and rectangles.

A rectangle is a convex quadrilateral because it has two diagonals and both lie in the interior of the rectangle.

Draw line AD and DC such that $AB \parallel CD$ and $AD \parallel BC$ .

$AD= BC$ and $AB= CD$

ABCD is a rectangle as it has opposite sides equal and parallel.

All angles of the rectangle are $90\degree$ and a rectangle has two diagonals equal and bisect each other.

Hence, AO = BO = CO = DO

$\therefore$ O is equidistant from A,B,C,D.

NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals - Topic: Rectangle

(1).All the properties of a parallelogram.

(2) Each of the angles is a right angle.

(3) Diagonals are equal

Class 8 understanding quadrilaterals NCERT Solutions - Topic: Square

Properties of the rectangle are :

(1) All the properties of a parallelogram.

(2) Each of the angles is a right angle.

(3) Diagonals are equal.

A square satisfies all the properties of rectangles so a square can be defined as a rectangle with all sides equal.

Properties of a rhombus are :

(1) All the properties of a parallelogram.

(2) Diagonals are perpendicular to each other.

A square satisfies all the properties of the rhombus so we can define it as
rhombus with equal angles.

NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals - Topic: Trapezium

Trapezium has two sides parallel and the other two sides are non-parallel. Parallel sides may be equal or unequal but we cannot have a trapezium with all sides and angles equal.

## Understanding Quadrilaterals Class 8 Solutions - Topics

• Polygons
• Sum of the Measures of the Exterior Angles of a Polygon
• Some Special Parallelograms

## NCERT Solutions for Class 8 Maths -Chapter Wise

 Chapter -1 Rational Numbers Chapter -2 Linear Equations in One Variable Chapter-3 Understanding Quadrilaterals Chapter-4 Practical Geometry Chapter-5 Data Handling Chapter-6 Squares and Square Roots Chapter-7 Cubes and Cube Roots Chapter-8 Comparing Quantities Chapter-9 Algebraic Expressions and Identities Chapter-10 Visualizing Solid Shapes Chapter-11 Mensuration Chapter-12 Exponents and Powers Chapter-13 Direct and Inverse Proportions Chapter-14 Factorization Chapter-15 Introduction to Graphs Chapter-16 Playing with Numbers

## Key Features of Understanding Quadrilaterals Class 8 NCERT Solutions

Clarity of Concepts: In this maths chapter 3 class 8 we are ocusing on clarifying the fundamental properties and properties of different types of quadrilaterals.

Real-Life Applications: Explaining how the concepts of quadrilaterals are applied in practical situations and in geometry.

Practice Questions: Additional practice problems to reinforce learning and problem-solving skills. Students can practice class 8 maths ch 3 question answer using the pdf.

### NCERT Solutions for Class 8: Subject-Wise

How to use NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals?

• Learn how to use their properties in specific questions using the solved examples.
• Practice the problems given in the NCERT textbook.
• During the practice, if you find a problem in solving any of the questions you can use NCERT solutions for Class 8 Maths chapter 3 Understanding Quadrilaterals.

Keep working hard and happy learning!

Also Check NCERT Books and NCERT Syllabus here:

1. What are the important topics of chapter Understanding Quadrilaterals ?

• when the lengths of four sides and a diagonal are given, when two diagonals and three sides are given
• When two adjacent sides and three angles are known
• When three sides and two included angles are given

are the important topics of this chapter.

2. How many chapters are there in the CBSE class 8 maths ?

There are 16 chapters starting from rational number to playing with numbers in the CBSE class 8 maths.

3. Does CBSE provides the solutions of NCERT for class 8 ?

No, CBSE doesn’t provide NCERT solutions for any class or subject.

4. Where can I find the complete solutions of NCERT for class 8 ?

Here you will get the detailed NCERT solutions for class 8 by clicking on the link.

5. How does the NCERT solutions are helpful ?

NCERT solutions are provided in a very detailed manner which will give the conceptual clarity to the students. Also, students can take help from these solutions when they are not able to solve them on their own.

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##### AWS Solution Architect

An AWS Solution Architect is someone who specializes in developing and implementing cloud computing systems. He or she has a good understanding of the various aspects of cloud computing and can confidently deploy and manage their systems. He or she troubleshoots the issues and evaluates the risk from the third party.

4 Jobs Available
##### Computer Programmer

Careers in computer programming primarily refer to the systematic act of writing code and moreover include wider computer science areas. The word 'programmer' or 'coder' has entered into practice with the growing number of newly self-taught tech enthusiasts. Computer programming careers involve the use of designs created by software developers and engineers and transforming them into commands that can be implemented by computers. These commands result in regular usage of social media sites, word-processing applications and browsers.

3 Jobs Available
##### Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.

3 Jobs Available
##### Information Security Manager

Individuals in the information security manager career path involves in overseeing and controlling all aspects of computer security. The IT security manager job description includes planning and carrying out security measures to protect the business data and information from corruption, theft, unauthorised access, and deliberate attack

3 Jobs Available
##### Big Data Analytics Engineer

Big Data Analytics Engineer Job Description: A Big Data Analytics Engineer is responsible for collecting data from various sources. He or she has to sort the organised and chaotic data to find out patterns. The role of Big Data Engineer involves converting messy information into useful data that is clean, accurate and actionable.

2 Jobs Available