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

Check out:

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.
A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is \(3/5\), then find the number of yellow balls.
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2.
The graph of \(y = f(x)\) is given. The number of zeroes of \(f(x)\) is :
- 0
- 1
- 3
- 2
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3.
The natural number 1 is :
- a prime number.
- a composite number.
- prime as well as composite.
- neither prime nor composite.
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4.
If \(PQ\) and \(PR\) are tangents to the circle with centre \(O\) and radius \(4 \text{ cm}\) such that \(\angle QPR = 90^{\circ}\), then the length \(OP\) is
- \(4 \text{ cm}\)
- \(4\sqrt{2} \text{ cm}\)
- \(8 \text{ cm}\)
- \(2\sqrt{2} \text{ cm}\)
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5.
PQ and PR are two tangents to a circle with centre O and radius 5 cm. AB is another tangent to the circle at C which lies on OP. If \(OP = 13\) cm, then find the length AB and PA.
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6.
The HCF of 960 and 432 is :
- 48
- 54
- 72
- 36
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