NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals Exercise 8.1 and Exercise 8.2 – चतुर्भुज की प्रश्नावली 8.1 and प्रश्नावली 8.2 in free PDF download in Hindi Medium and English Medium for all the students following NCERT Books for the academic session 2019-20. 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.
| Class 9: | Maths – गणित |
| Chapter 8: | Quadrilaterals |
Table of Contents
- 1 NCERT Solutions for Class 9 Maths Chapter 8
- 1.1 Class 9 Maths Chapter 8 Quadrilaterals Solutions
- 1.2 9 Maths Chapter 8 Exercise 8.1 & 8.2 Solutions in Video
- 1.2.1 The angles of quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral.
- 1.2.2 ABCD एक चतुर्भुज है जिसमें P, Q, R और S क्रमशः भुजाओं AB, BC, CD और DA के मध्य-बिंदु हैं । AC उसका एक विकर्ण है। दर्शाइए कि SR || AC और SR=1/2 AC है।
- 1.2.3 If the diagonals of a parallelogram are equal, then show that it is a rectangle.
- 1.2.4 Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.
- 1.2.5 ABC एक त्रिभुज है जिसका कोण C समकोण है। कर्ण AB के मध्य-बिंदु M से होकर BC के समांतर खींची गई रेखा AC को D पर प्रतिच्छेद करती है। दर्शाइए कि D भुजा AC का मध्य-बिंदु है।
NCERT Solutions for Class 9 Maths Chapter 8
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Class 9 Maths Chapter 8 Quadrilaterals Solutions
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Class 9 Maths Chapter 8 Exercise 8.1 Solutions in English
NCERT Solutions for Class 9 Maths Chapter 8 Exercise 8.1 sols in English medium for CBSE, UP Board, Uttarakhand, Bihar and Gujrat board, wherever the NCERT Books are prescribed as a course book. See here Exercise 8.2 and Hindi Medium or View in Video Format for the students using books in Hindi. Download Class 9 Maths App for Offline use.
Class 9 Maths Chapter 8 Exercise 8.2 Solutions in English
9 Maths Exercise 8.2 Solutions in English medium free to use for all the students as well as teachers. Move to Exercise 8.1 or View in Video Format or to in Hindi Medium as per your need. Download Class 9 Maths App for Offline use.
9 Maths Chapter 8 Exercise 8.1 Solutions in Hindi
9 Maths Exercise 8.1 Solutions in Hindi Medium free to download or use it ONLINE. Click here if you want to study प्रश्नावली 8.2 or View in Video Format or go for English Medium if you want to change the medium. Download कक्षा 9 गणित App for offline use.
9 Maths Chapter 8 Exercise 8.2 Solutions in Hindi
NCERT Books Solutions for Class 9 Ganit PRASHNAVALI 8.2 in Hindi free to use offline as well as online. Visit here for चतुर्भुज की प्रश्नावली 8.1 and for solutions in English or View in Video Format click here English Medium. Download कक्षा 9 गणित App for offline use.
9 Maths Chapter 8 Exercise 8.1 & 8.2 Solutions in Video
NCERT Solutions for class 9 Maths Exercise 8.1 in video format with complete description. Download Class 9 Maths App for Offline use or Download कक्षा 9 गणित App for offline use.
NCERT Solutions for class 9 Maths Exercise 8.2 in video format with complete description.
Important Theorems and Rules on Quadrilaterals
- Sum of the all angles of a quadrilateral is 360.
- A quadrilateral in which one pair of opposite sides are parallel, is called trapezium.
- A quadrilateral in which both pairs of opposite sides are parallel, is called parallelogram.
- A parallelogram in which one of its angle is right angle, is called a rectangle.
- A parallelogram in which all side are equal, is called rhombus.
- A rectangle with all sides equal, is a square.
- Diagonals of parallelogram divides it into two congruent triangles.
- In a parallelogram
- Opposite sides are equal
- Opposite angles are equal
- Diagonals bisect each other.
- The diagonals of following quadrilateral bisect each other:
- Parallelogram
- Rectangle
- Square
- Rhombus
- The line segment joining the mid-points of two sides of a triangle is parallel to the third side and is half of it.
- A line drawn through the mid-point of a side of a triangle parallel to another side bisects the third side.
The quadrilateral formed by joining the mid-points of the sides of a quadrilateral, taken in order, is a parallelogram.
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Table of Contents
- 1 The angles of quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral.
- 2 ABCD एक चतुर्भुज है जिसमें P, Q, R और S क्रमशः भुजाओं AB, BC, CD और DA के मध्य-बिंदु हैं । AC उसका एक विकर्ण है। दर्शाइए कि SR || AC और SR=1/2 AC है।
- 3 If the diagonals of a parallelogram are equal, then show that it is a rectangle.
- 4 Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.
- 5 ABC एक त्रिभुज है जिसका कोण C समकोण है। कर्ण AB के मध्य-बिंदु M से होकर BC के समांतर खींची गई रेखा AC को D पर प्रतिच्छेद करती है। दर्शाइए कि D भुजा AC का मध्य-बिंदु है।
The angles of quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral.
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°
ABCD एक चतुर्भुज है जिसमें P, Q, R और S क्रमशः भुजाओं AB, BC, CD और DA के मध्य-बिंदु हैं । AC उसका एक विकर्ण है। दर्शाइए कि SR || AC और SR=1/2 AC है।
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]
If the diagonals of a parallelogram are equal, then show that it is a rectangle.
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.
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.
ABC एक त्रिभुज है जिसका कोण C समकोण है। कर्ण AB के मध्य-बिंदु M से होकर BC के समांतर खींची गई रेखा AC को D पर प्रतिच्छेद करती है। दर्शाइए कि D भुजा AC का मध्य-बिंदु है।
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]