NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals in English Medium and Hindi Medium updated for new academic session 2023-24. Educational platform Tiwari Academy including apps, incorporate visual aids like diagrams, graphs, and charts to illustrate mathematical concepts. Visual aids can enhance understanding and retention, especially for visual learners.

**Class 9 Maths Chapter 8 Solutions in English Medium**

Class 9 Maths Exercise 8.1 in English

Class 9 Maths Exercise 8.2 in English

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**Class 9 Maths Chapter 8 Solutions in Hindi Medium**

Class 9 Maths Exercise 8.1 in Hindi

Class 9 Maths Exercise 8.2 in Hindi

## NCERT Solutions for Class 9 Maths Chapter 8

Class: 9 | Mathematics |

Chapter: 8 | NCERT Solutions and Extra Questions |

Number of Exercises: | 2 (Two) |

Topic: | Quadrilaterals |

Content Mode: | Videos and Text |

Session: | Academic Year 2023-24 |

Medium: | English and Hindi Medium |

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 are in Hindi Medium and English Medium for all the students following NCERT Books for the academic session 2023-24. NCERT (https://ncert.nic.in/) 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 Class 9 Maths Chapter 8

### 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 2023-24 are prescribed as a course book. Download Offline Apps for session 2023-24, which work well even without internet.

#### Class 9 Maths Exercise 8.1 Solution in Hindi Medium

### Class 9 Maths Chapter 8 Practice Questions with 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.

### Important Questions on 9th Maths Chapter 8

### 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.

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.

### 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:

- The floor.
- Walls.
- Ceiling.
- Windows of your classroom.
- The blackboard.
- Each face of the duster.
- Each page of your book.
- 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.