NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals Exercise 8.1 and Exercise 8.2 in English Medium and Hindi Medium updated for new academic session 2022-2023. Download Prashnavali 8.1 and Prashnavali 8.2 in Hindi Medium with videos.

## Class 9 Maths Chapter 8 All Exercises Solutions

### NCERT Solutions for Class 9 Maths Chapter 8

UP Board students are now using NCERT Books for UP board course. So, they also take the help from these 9th Maths solutions. Download UP Board Solutions for class 9 Maths Chapter 8 in Hindi Medium free. Class 9 Maths Solutions 2022-2023 are in Hindi Medium and English Medium for all the students following NCERT Books 2022-23 for the academic session 2022-2023. NCERT Solutions for all other subjects are also available in downloadable form. Videos related to each questions and Ex. 8.1 and Ex. 8.2 are also given with complete descriptions. Download Class 9 Maths App for Offline use or Download Kaksha 9 Ganit App for offline use.

• ### Study Material for Session 2022-2023

 Class: 9 Maths (English and Hindi Medium) Chapter 8: Quadrilaterals

### 9th Maths Chapter 8 Solutions in English & Hindi Medium

NCERT Solutions for Class 9 Maths Chapter 8 Exercise 8.1 & 8.2 sols in English as well as medium for CBSE, UP Board, Uttarakhand, Bihar and Gujrat board, wherever the NCERT Books 2022-23 are prescribed as a course book. Download Offline Apps for session 2022-23, which work well even without internet.

#### Class 9 Maths Exercise 8.1 Solutions in Videos

Class 9 Maths Exercise 8.1 Question 1, 2 Solutions
Class 9 Maths Exercise 8.1 Question 3, 4 Solutions

#### Class 9 Maths Exercise 8.2 Solution in Videos

Class 9 Maths Exercise 8.2 Question 1 Solution
Class 9 Maths Exercise 8.2 Question 2 Solution

### What are the properties of a parallelogram?

In a parallelogram
Opposite sides are equal
Opposite angles are equal
Diagonals bisect each other.

### In which type of quadrilaterals, diagonals bisect each other?

The diagonals of following quadrilateral bisect each other:
Parallelogram
Rectangle
Square
Rhombus

#### Important Notes on 9th Maths Chapter 8

1. Sum of the all angles of a quadrilateral is 360.
2. A quadrilateral in which one pair of opposite sides are parallel, is called trapezium.
3. A quadrilateral in which both pairs of opposite sides are parallel, is called parallelogram.
4. A parallelogram in which one of its angle is right angle, is called a rectangle.
5. A parallelogram in which all side are equal, is called rhombus.
6. A rectangle with all sides equal, is a square.
7. Diagonals of parallelogram divides it into two congruent triangles.
8. The line segment joining the mid-points of two sides of a triangle is parallel to the third side and is half of it.
9. A line drawn through the mid-point of a side of a triangle parallel to another side bisects the third side.
10. The quadrilateral formed by joining the mid-points of the sides of a quadrilateral, taken in order, is a parallelogram.

### The angles of quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral.

Let the first angle = 3x
Therefore,
the second angle = 5x,
Third angle = 9x and
Fourth angle = 13x
Sum of all angles of a quadrilateral is 360°.
Therefore, 3x + 5x + 9x + 13x = 360°
⇒ 30x = 360°
⇒ x = (360°)/30 =12°
Hence,
The first angle = 3 × 12° =36°,
The second angle = 5 × 12° = 60°,
Third angle = 9 × 12° = 108°
The forth angle = 13 × 12° = 156°

### If the diagonals of a parallelogram are equal, then show that it is a rectangle.

Given: ABCD is a parallelogram with AC = BD.
To Prove: ABCD is a rectangle.
Solution: In ΔABC and ΔBAD,
BC = AD [∵ Opposite sides of a parallelogram are equal]
AC = BD [∵ Given] AB = AB [∵ Common]
Hence, ΔABC ≅ ΔBAD [∵SSS Congruency rule]
∠ABC = ∠BAD [∵ CPCT] But, ∠ABC + ∠BAD = 180° [∵ Co-interior angles]
⇒ 2∠BAD = 180° [∵ ∠ABC = ∠BAD]
⇒ ∠BAD = (180°)/2 = 90°
A parallelogram with one of its angle is 90° is a rectangle.
Hence, ABCD is a rectangle.

### Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

Given: ABCD is a quadrilateral in which AO = CO, BO = DO and ∠COD = 90°.
To prove: ABCD is a rhombus.
Solution: In ΔAOB and ΔAOD,
BO = DO [∵ Given]
∠AOB = ∠AOD [∵ Each 90°]
AO = AO [∵ Common]
Hence, ΔAOB ≅ ΔAOD [∵SAS Congruency rule]
AB = AD [∵ CPCT]
Similarly, AB = BC and BC = CD
Now, all the four sides of quadrilateral ABCD are equal.
Hence, ABCD is a rhombus.

### How many questions and examples are there in chapter 8, Quadrilaterals of 9th Maths?

Chapter 8 Quadrilaterals of 9th Maths has two exercises. In the first exercise (Ex 8.1), there are 6 examples and 12 questions. The second exercise (Ex 8.2) contains two examples and 7 questions. So, there are 8 examples and 19 questions in chapter 8.

### What are the main topics that students will study in chapter 8 of grade 9th Maths?

Topics that students will study in chapter 8 of grade 9th Maths are:

• 1. Meaning of quadrilateral.
• 2. Angle sum property of a quadrilateral.
• 3. Types of quadrilateral (Trapezium, Parallelogram, Rectangle, Rhombus, Square, Kite).
• 4. Area of a Parallelogram.
• 5. Properties of a parallelogram.
• 6. The Mid-point theorem.
• 7. The converse of Mid-point theorem.

### What are some real-life examples in Chapter 8 of 9th Maths quadrilaterals?

Some real-life examples of quadrilaterals are:

1. The floor.
2. Walls.
3. Ceiling.
4. Windows of your classroom.
5. The blackboard.
6. Each face of the duster.
7. Each page of your book.
8. The top of your study table.

### Is chapter 8 Quadrilaterals of class 9th Maths easy or difficult to solve and understand?

Chapter 8 of class 9th maths is a little difficult to solve and understand because this chapter contains proving questions. However, the difficulty level of any topic varies from student to student. So, Chapter 8 of class 9th maths is easy or difficult depends on students also. Some students find it difficult, and some find it easy.

### Does chapter 8 of class 9th Maths contain any theorem?

Yes, chapter 8 of class 9th Maths contains theorems. There are ten theorems in chapter 8. All the theorems are nice and easy.