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.
The HCF of 960 and 432 is :
- 48
- 54
- 72
- 36
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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.
There are two sections A and B of Grade X. There are 28 students in Section A and 30 students in Section B. What is the minimum number of books you will acquire for the class library so that they can be distributed equally among students of Section A or Section B ?
- 144
- 2
- 420
- 272
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4.
In a class test, the sum of Anamika's marks obtained in Maths and Science is 30. Had she got 2 marks more in Maths and 3 marks less in Science, the product of the marks would have been 210. Find the marks she got in the two subjects.
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5.
\(ABCD\) is a parallelogram such that \(AF = 7 \text{ cm}\), \(FB = 3 \text{ cm}\) and \(EF = 4 \text{ cm}\), length \(FD\) equals
- \(\frac{21}{4} \text{ cm}\)
- \(\frac{28}{3} \text{ cm}\)
- \(\frac{12}{7} \text{ cm}\)
- \(5.5 \text{ cm}\)
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6.
If the quadratic equation \(9x^2 + 8kx + 16 = 0\) has real and equal roots, then the value of k is
- 3
- –3
- –4
- \(\pm 3\)
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