NCERT Solutions for Class 9 Maths Chapter 8 : Quadrilaterals

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The NCERT Solutions for Class 9 Mathematics have been provided in this article. Quadrilaterals include more than one type of shape, but all quadrilaterals have four sides. The most common type of quadrilateral is square, but rectangles and rhombuses are considered quadrilaterals too. Quadrilaterals are also called quadrangles and tetragons.

Class 9 Maths Chapter 8 Quadrilaterals belong to Unit 4 Geometry which has a weightage of 27 marks in the Class 9 Maths Examination. NCERT Solutions for Class 9 Maths for Chapter 8 cover the following important concepts:

Download: NCERT Solutions for Class 9 Mathematics Chapter 8 pdf

NCERT Solutions for Class 9 Maths Chapter 8

Important Topics in Class 9 Maths Chapter 8 Quadrilaterals

Important Topics in Class 9 Maths Chapter 8 Quadrilaterals are elaborated below:

Cyclic Quadrilateral

Cyclic quadrilateral is a type of quadrilateral which has all of its four vertices lying on the circumference of a circle. Cyclic quadrilteral is a unique four-sided quadrilateral circumscribed in a circle.

Important Points of a Cyclic Quadrilateral:

The sides of a cyclic quadrilateral that are found to touch the circumference of a circle are the same four chords of the circle.
Area of a cyclic quadrilateral = √(s−a)(s−b)(s−c)(s−d) where a, b, c, and d are the four sides and S is the semi perimeter.
Perimeter of a cyclic quadrilateral = 2S, where S = (1/2) × (a + b + c + d)

Quadrilateral Angle Sum Property

Quadrilateral Angle sum property states that the sum of all four interior angles is equal to 360^o.

Example: Assume that the sum of three interior angles of a quadrilateral is 240^o. With the given data, determine its fourth angle.

Solution: First, consider that the fourth angle is x
Now, since the sum of four interior angles of a quadrilateral is 360^o, we can say,
⇒ x + 240^o = 360^o
⇒ x = 120^o

Perimeter of a Paralellogram

The perimeter of a parallelogram can be defined as the sum of the total distance outside its shape. A paralellogram is a four-sided polygon with parallel sides that never intersect.

Perimeter of Paralellogram Formula:
Perimeter of parallelogram = a + b + c + d
⇒ 2a + 2b= 2(a+b)
⇒ P = 2(a+b).

NCERT Solutions for Class 9 Maths Chapter 8 Exercises:

The detailed solutions for all the NCERT Solutions for Quadrilaterals under different exercises are:

Also Read:

Unit Related Topics
Quadrilateral formulas	Types of Quadrilaterals	Properties of a Parallelogram
Difference between Rhombus and Parallelogram	Area of a Trapezoid Formula	Tangential Quadrilateral Formula
Class 9 Maths Chapter 8 Quadrilaterals MCQs	Angles of a Parallelogram	Area of a Square

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Math Study Guides
Maths Important Formulas	Maths MCQs	Comparison Articles in Maths
Difference Between Topics in Maths	Math Study Material	Algebra
Trigonometry	Number Systems	Mensuration
Math Formula	NCERT Solutions for Class 9 Maths	Geometry

CBSE X Related Questions

1.
The number of red balls in a bag is three more than the number of black balls. If the probability of drawing a red ball at random from the given bag is $\dfrac{12}{23}$, find the total number of balls in the given bag.
View Solution
2.
Using prime factorisation, find the HCF of 144, 180 and 192.
View Solution
3.
The following data shows the number of family members living in different bungalows of a locality:

Number of Members 0−2 2−4 4−6 6−8 8−10 Total
Number of Bungalows 10 p 60 q 5 120

If the median number of members is found to be 5, find the values of p and q.
View Solution
4.
A peacock sitting on the top of a tree of height 10 m observes a snake moving on the ground. If the snake is $10\sqrt{3}$ m away from the base of the tree, then angle of depression of the snake from the eye of the peacock is
- $60^\circ$
- $45^\circ$
- $30^\circ$
- $90^\circ$
View Solution
5.
In the adjoining figure, TP and TQ are tangents drawn to a circle with centre O. If $\angle OPQ = 15^\circ$ and $\angle PTQ = \theta$, then find the value of $\sin 2\theta$.
View Solution
6.
Let $p$, $q$ and $r$ be three distinct prime numbers. Check whether $pqr + q$ is a composite number or not. Further, give an example for three distinct primes $p$, $q$, $r$ such that
(i) $pqr + 1$ is a composite number
(ii) $pqr + 1$ is a prime number
View Solution

Number of Members	0−2	2−4	4−6	6−8	8−10	Total
Number of Bungalows	10	p	60	q	5	120

View All

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You can also check

NCERT Solutions for Class 9 Maths Chapter 8 : Quadrilaterals

NCERT Solutions for Class 9 Maths Chapter 8

Important Topics in Class 9 Maths Chapter 8 Quadrilaterals

Cyclic Quadrilateral

Quadrilateral Angle Sum Property

Perimeter of a Paralellogram

NCERT Solutions for Class 9 Maths Chapter 8 Exercises:

CBSE X Related Questions

1.
The number of red balls in a bag is three more than the number of black balls. If the probability of drawing a red ball at random from the given bag is $\dfrac{12}{23}$, find the total number of balls in the given bag.

2.
Using prime factorisation, find the HCF of 144, 180 and 192.

3.
The following data shows the number of family members living in different bungalows of a locality:

Number of Members 0−2 2−4 4−6 6−8 8−10 Total
Number of Bungalows 10 p 60 q 5 120

If the median number of members is found to be 5, find the values of p and q.

4.
A peacock sitting on the top of a tree of height 10 m observes a snake moving on the ground. If the snake is $10\sqrt{3}$ m away from the base of the tree, then angle of depression of the snake from the eye of the peacock is

5.
In the adjoining figure, TP and TQ are tangents drawn to a circle with centre O. If $\angle OPQ = 15^\circ$ and $\angle PTQ = \theta$, then find the value of $\sin 2\theta$.

6.
Let $p$, $q$ and $r$ be three distinct prime numbers. Check whether $pqr + q$ is a composite number or not. Further, give an example for three distinct primes $p$, $q$, $r$ such that
(i) $pqr + 1$ is a composite number
(ii) $pqr + 1$ is a prime number

Similar Mathematics Concepts

Comments

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NCERT Solutions for Class 9 Maths Chapter 8 : Quadrilaterals

NCERT Solutions for Class 9 Maths Chapter 8

Important Topics in Class 9 Maths Chapter 8 Quadrilaterals

Cyclic Quadrilateral

Quadrilateral Angle Sum Property

Perimeter of a Paralellogram

NCERT Solutions for Class 9 Maths Chapter 8 Exercises:

CBSE X Related Questions

1.The number of red balls in a bag is three more than the number of black balls. If the probability of drawing a red ball at random from the given bag is $\dfrac{12}{23}$, find the total number of balls in the given bag.

2.Using prime factorisation, find the HCF of 144, 180 and 192.

3.The following data shows the number of family members living in different bungalows of a locality: Number of Members0−22−44−66−88−10TotalNumber of Bungalows10p60q5120If the median number of members is found to be 5, find the values of p and q.

4.A peacock sitting on the top of a tree of height 10 m observes a snake moving on the ground. If the snake is $10\sqrt{3}$ m away from the base of the tree, then angle of depression of the snake from the eye of the peacock is

5.In the adjoining figure, TP and TQ are tangents drawn to a circle with centre O. If $\angle OPQ = 15^\circ$ and $\angle PTQ = \theta$, then find the value of $\sin 2\theta$.

6.Let $p$, $q$ and $r$ be three distinct prime numbers. Check whether $pqr + q$ is a composite number or not. Further, give an example for three distinct primes $p$, $q$, $r$ such that (i) $pqr + 1$ is a composite number (ii) $pqr + 1$ is a prime number

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
The number of red balls in a bag is three more than the number of black balls. If the probability of drawing a red ball at random from the given bag is $\dfrac{12}{23}$, find the total number of balls in the given bag.

2.
Using prime factorisation, find the HCF of 144, 180 and 192.

3.
The following data shows the number of family members living in different bungalows of a locality:

Number of Members 0−2 2−4 4−6 6−8 8−10 Total
Number of Bungalows 10 p 60 q 5 120

If the median number of members is found to be 5, find the values of p and q.

4.
A peacock sitting on the top of a tree of height 10 m observes a snake moving on the ground. If the snake is $10\sqrt{3}$ m away from the base of the tree, then angle of depression of the snake from the eye of the peacock is

5.
In the adjoining figure, TP and TQ are tangents drawn to a circle with centre O. If $\angle OPQ = 15^\circ$ and $\angle PTQ = \theta$, then find the value of $\sin 2\theta$.

6.
Let $p$, $q$ and $r$ be three distinct prime numbers. Check whether $pqr + q$ is a composite number or not. Further, give an example for three distinct primes $p$, $q$, $r$ such that
(i) $pqr + 1$ is a composite number
(ii) $pqr + 1$ is a prime number