NCERT Solutions for Class 9 Maths Chapter 8
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 2020-21 based on latest NCERT Books of new session.
Download चतुर्भुज की प्रश्नावली 8.1 and प्रश्नावली 8.2 in Hindi Medium free PDF download for academic session 2020-21. Class 9 Maths Solutions 2020-2021 are in Hindi Medium and English Medium for all the students following NCERT Books 2020-21 for the academic session 2020-2021. NCERT Solutions for all other subjects are also available in downloadable form. Download Class 9 Maths App for Offline use or Download कक्षा 9 गणित App for offline use.NCERT Solutions for Class 9 Maths Chapter 8
| Class: | 9 |
| Subject: | Maths – गणित |
| 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 2020-21 are prescribed as a course book. Download Offline Apps for session 2020-21, which work well even without internet.
9th Maths Exercise 8.1 Solutions
9th Maths Exercise 8.2 Solutions
Study Material
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.
Important Questions on 9th Maths Chapter 8
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°
S भुजा DA का मध्य-बिंदु हैं [∵ दिया है]
R भुजा DC का मध्य-बिंदु हैं [∵ दिया है]
अतः, SR || AC और SR = 1/2 AC
[∵ मध्य-बिंदु प्रमेय]
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.
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.
M भुजा AB का मध्य-बिंदु है [∵ दिया है]
तथा DM || BC [∵ दिया है]
अतः, D भुजा AC का मध्य-बिंदु होगा [∵ मध्य-बिंदु प्रमेय के विलोम से]
