# NCERT Solutions for Class 9 Maths Chapter 8 – Quadrilaterals

NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals will help you in solving all the difficult questions of the Chapter in minutes. By preparing the NCERT Solutions for this Chapter you can revise the basic properties quadrilaterals such as parallelograms, rhombus etc. This Chapter of NCERT Solutions for Class 9 Maths also includes an extension of the angle sum property of triangles to the angle sum property of quadrilaterals. The Midpoint Theorem is one of the most important and scoring topics of this Chapter.

You are given a total of 19 questions to solve in 2 Exercises in the Class 9 Maths NCERT Chapter 8. Some questions of the NCERT exercises require you to verify theorems while some require you to find the values of certain angles. These questions are very inquisitive in nature and you might take some time in solving them. Therefore, it is highly recommended that you go through the Maths NCERT Solutions for Class 9 Chapter 8 extensively to save your time.

Solving CBSE NCERT Maths Exercises in Class 9 is a great practice as it helps you understand the Chapter thoroughly. Concepts like Properties of Parallelograms, Conditions when a Quadrilateral becomes a Parallelogram, Conditions when a Parallelogram becomes a Rhombus and the Midpoint Theorem will become much clear after solving the NCERT Exercises of Chapter 8. Our subject matter experts have prepared a quick summary of Chapter 8 for you along with the NCERT Solutions.

## Important Points of NCERT Solutions for Class 9 Maths Chapter 8

**Introduction to Quadrilaterals:**

- A figure formed by joining four points in order is known as a Quadrilateral.
- A Quadrilateral has 4 sides, 4 angles and 4 vertices.

**Angle Sum Property of a Quadrilateral:**

The sum of all the angles of a quadrilateral is 360°.

**Types of Quadrilaterals:**

- When one pair of opposite sides of a quadrilateral are parallel, then the quadrilateral is known as a trapezium.
- When both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is known as a parallelogram.
- When in a parallelogram, one of its angles is a right angle, then the parallelogram is known as a rectangle.
- The parallelogram that has all sides equal is called a rhombus.
- The parallelogram that has one right angle and all sides equal in length is known as a square.
- When two pairs of adjacent sides are equal and it is not a parallelogram, then the quadrilateral is called a kite.

Note:

- A square is a rectangle and a rhombus but vice versa is not true
- A parallelogram is a trapezium but vice versa is not true.
- A kite is not a parallelogram.

**Properties of a Parallelogram:**

- If we draw a diagonal in a parallelogram, the parallelogram will be divided into two congruent triangles.
- The opposite sides of a parallelogram are equal to one another.
- In a situation, when we find that the opposite sides of a quadrilateral are equal, it is certain that it is a parallelogram.
- Each pair of the opposite angles are equal in a parallelogram
- If all the pairs of opposite angles are found to be equal in a given quadrilateral, then the quadrilateral is a parallelogram.
- The diagonals in a parallelogram divide each other into two equal halves, that is, they bisect each other.
- If the diagonals of a quadrilateral divide one another into equal halves, then the quadrilateral is said to be a parallelogram.
- If in a quadrilateral, only one pair of opposite sides and opposite angles are equal simultaneously, then it is said to be a parallelogram.
- Mid-Point Theorem:

(i) If we draw a line segment from the mid-point of one side of a triangle parallelly to another side, then this line segment will bisect the third side of the given triangle.

(ii) The line drawn through the mid-points of two sides of a triangle is parallel to the third side of the given triangle.

## Key points of CBSE Class 9 NCERT Maths Chapter 8 Quadrilaterals:

- The sum of all interior angles in a quadrilateral is 360°.
- A parallelogram is divided into two congruent triangles by a diagonal.
- Diagonals in a rectangle are equal and divide one another into two equal halves.
- Diagonals of a rhombus divide each other into equal halves and make an angle of 90°.
- Diagonals of a square are equal in length and divide each other into equal halves while making an angle of 90° at the point of intersection.

## Exercise Wise Discussion of NCERT Solutions for Class 9 Maths Chapter 8

- The exercise Solutions of the NCERT Class 9 Maths Chapter 8 are curated in such a way that you can get all your doubts related to the chapter sorted at one place.
- CBSE Class 9 Maths Chapter 8 exercise 8.1 solutions include 12 questions where you will have to find the values of angles and prove some theorems through logical reasoning and concepts that you learned in previous chapters.
- CBSE Class 9 Maths Chapter 8 exercise 8.2 solutions include 7 questions. You will have to show that a given quadrilateral is a parallelogram, a rectangle and a rhombus respectively. One question of the Midpoint Theorem is also included in the exercise.
- The questions in Chapter 8 of CBSE NCERT Class 9 Maths book will make you recall the concepts and theorems extensively to help you in an in-depth revision of geometry concepts.
- Practising the exercise solutions of the second exercise will help you learn new properties related to quadrilaterals. You can apply these properties to solve more complicated problems in exams like NTSE or other competitive exams.

## Benefits of NCERT Solutions for Class 9 Maths Chapter 8 provided by Instasolv

- All the NCERT Solutions for Class 9 Maths Chapter 8 are created as per the CBSE exam pattern and syllabus.
- The Maths NCERT Exercise Solutions for Class 9 Chapter 8 covers each and every topic and all the questions with a holistic approach.
- With these NCERT Solutions for Class 9 Maths Chapter 8, you will be able to solve a variety of questions in your CBSE exams related to Quadrilaterals.