NCERT Solutions for Class 9 Maths Chapter 7

NCERT Solutions for Class 9 Maths Chapter 7 Triangles Exercise 7.1, Exercise 7.2, Exercise 7.3, Exercise 7.4 and Exercise 7.5 – त्रिभुज की प्रश्नावली 7.1, प्रश्नावली 7.2, प्रश्नावली 7.3, प्रश्नावली 7.4 और प्रश्नावली 7.5 in PDF form to free download in Hindi Medium and English Medium or View in Video Format for the students studying NCERT Books based on the CBSE Curriculum 2019-20. Download Class 9 Maths App for Offline use or Download कक्षा 9 गणित App for offline use.




Class 9:Maths – गणित
Chapter 7:Triangles

NCERT Solutions for Class 9 Maths Chapter 7 Triangles - त्रिभुज

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NCERT Solutions for Class 9 Maths Chapter 7

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Class 9 Maths Chapter 7 Triangles त्रिभुज Solutions

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9 Maths Chapter 7 Exercise 7.1 in English

NCERT Solutions for class 9 Maths Exercise 7.1 in English medium free download. For the solutions of other exercises click here Exercise 7.2, Exercise 7.3, Exercise 7.4 and Exercise 7.5 or View in Video Format If you need solutions in Hindi, go for Hindi Medium. Download Class 9 Maths App for Offline use.

NCERT Solutions for class 9 Maths Exercise 7.1 in English medium

NCERT Solutions for class 9 Maths Exercise 7.1 in English medium PDF

NCERT Solutions for class 9 Maths Exercise 7.1 in English medium updated for 2018-19

9 Maths Chapter 7 Exercise 7.2 in English

NCERT Solutions for Class 9 Maths chap. 7 Triangles Exercise 7.2 in English medium. Other exercises of Triangles sols are Exercise 7.1, Exercise 7.3, Exercise 7.4 and Exercise 7.5 or View in Video Format In case you want sols in Hindi click go for Hindi Medium solutions. Download Class 9 Maths App for Offline use.




Class 9 Maths chap. 7 Triangles Exercise 7.2 in English medium

Class 9 Maths chap. 7 Triangles Exercise 7.2 in English medium solutions for all boards

Class 9 Maths chap. 7 Triangles Exercise 7.2 in English medium sols for up board, gujrat board and cbse

9 Maths Chapter 7 Exercise 7.3 in English



NCERT Solutions for class 9 Maths Chapter 7 Triangles Ex. 7.3 in English medium. See more questions in other exercises Exercise 7.1, Exercise 7.2, Exercise 7.4 and Exercise 7.5 or View in Video Format and click Hindi Medium for sols in Hindi. Download Class 9 Maths App for Offline use.

NCERT Solutions for class 9 Maths Chapter 7 Triangles Ex. 7.3 in English medium

NCERT Solutions for class 9 Maths Chapter 7 Triangles Ex. 7.3 in English medium in PDF

9 Maths Chapter 7 Exercise 7.4 in English

NCERT Solutions for class 9 Maths Exercise 7.4 in English medium. Click for the solutions of Exercise 7.1, Exercise 7.2, Exercise 7.3 and Exercise 7.5 or View in Video Format or Click Hindi Medium for sols in Hindi. Download Class 9 Maths App for Offline use.

NCERT Solutions for class 9 Maths Exercise 7.4 in English medium

NCERT Solutions for class 9 Maths Exercise 7.4 in English medium free in pdf

9 Maths Chapter 7 Exercise 7.5 in English




NCERT Solutions for class 9 Maths Chapter 7 Triangles Optional Exercise 7.5 in English medium. Move to Exercise 7.1, Exercise 7.2, Exercise 7.3 and Exercise 7.4 or View in Video Format and see here Hindi Medium solutions. Download Class 9 Maths App for Offline use.

9 Maths Chapter 7 Triangles Optional Exercise 7.5 in English medium

Class 9 Maths Exercise 7.1 in Hindi

NCERT Solutions for class 9 Maths Exercise 7.1 in Hindi medium. Move here for प्रश्नावली 7.2, प्रश्नावली 7.3, प्रश्नावली 7.4 और प्रश्नावली 7.5 to see online or View in Video Format . If your medium of study is English, click for English Medium to see the answers in English. Download कक्षा 9 गणित App for offline use.

NCERT Solutions for class 9 Maths Exercise 7.1 in Hindi medium

NCERT Solutions for class 9 Maths Exercise 7.1 in Hindi medium in PDF

NCERT Solutions for class 9 Maths Exercise 7.1 in Hindi medium updated for up board 2018-19

Class 9 Maths Exercise 7.2 in Hindi




9 Maths Exercise 7.2 Triangles solutions in Hindi Medium free to download. See the sols of other exercises प्रश्नावली 7.1, प्रश्नावली 7.3, प्रश्नावली 7.4 और प्रश्नावली 7.5 online use or View in Video Format. Move to English Medium sols for English medium students. Download कक्षा 9 गणित App for offline use.

9 Maths Exercise 7.2 Triangles solutions in Hindi Medium

9 Maths Exercise 7.2 Triangles solutions in Hindi Medium for up board

9 Maths Exercise 7.2 Triangles solutions in Hindi Medium Gujrat and Bihar board

Class 9 Maths Exercise 7.3 in Hindi

NCERT Solutions for class 9 Maths Exercise 7.3 in Hindi medium. See here the question-answers of प्रश्नावली 7.1, प्रश्नावली 7.2, प्रश्नावली 7.4 और प्रश्नावली 7.5 ONLINE or View in Video Format . Students using NCERT Books in English, click for English Medium sols. Download कक्षा 9 गणित App for offline use.

NCERT Solutions for class 9 Maths Exercise 7.3 in Hindi medium



NCERT Solutions for class 9 Maths Exercise 7.3 in Hindi medium in PDF

NCERT Solutions for class 9 Maths Exercise 7.3 in Hindi medium free for cbse and up board

Class 9 Maths Exercise 7.4 in Hindi

9 Maths Exercise 7.4 solutions in Hindi medium free for all students (UP Board, CBSE, Bihar, Uttarakhand and Gujrat Secondary Education Board) using NCERT Books. See other exercises here प्रश्नावली 7.1, प्रश्नावली 7.2, प्रश्नावली 7.3, और प्रश्नावली 7.5 or View in Video Format and go for English Medium to use it in English. Download कक्षा 9 गणित App for offline use.

9 Maths Exercise 7.4 solutions in Hindi medium



9 Maths Exercise 7.4 solutions in Hindi medium for CBSE, UP Board

Class 9 Maths Exercise 7.5 in Hindi

9 Maths Chapter 7 Optional Exercise 7.5 in Hindi medium free to use without any login password. Move to other exercises प्रश्नावली 7.1, प्रश्नावली 7.2, प्रश्नावली 7.3 और प्रश्नावली 7.4 or View in Video Format and see the solutions in English here English Medium sols. Download कक्षा 9 गणित App for offline use.

9 Maths Chapter 7 Optional Exercise 7.5 in Hindi medium

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9 Maths Chapter 7 Exercise 7.1, 7.2, 7.3, 7.4 & 7.5 Sols in Video

NCERT Solutions for class 9 Maths Exercise 7.1 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 7.2 in video format with complete description.

NCERT Solutions for class 9 Maths Exercise 7.3 in video format with complete description.

NCERT Solutions for class 9 Maths Exercise 7.4 in video format with complete description.

NCERT Solutions for class 9 Maths Exercise 7.5 in video format with complete description.

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Important Terms and Theorems on Triangles
  • Triangle: A plane figure closed by three intersecting lines is called a triangle. Here, ‘Tri’ means THREE. A triangle has three sides, three angles and three vertices.
  • Congruence of Triangle: Two triangles are congruent, if sides and angles of one triangle are equal to the corresponding sides and angles of the other triangle.
    • SSS (Side – Side – Side) Congruence Rule: Two triangles are congruent, if three sides of one triangle are equal to three sides of the other triangle.
    • RHS (Right angle – Hypotenuse – Side) Congruence Rule: Two right triangles are congruent, if the hypotenuse and one side of one triangle are equal to hypotenuse and one side of the other triangle.
    • ASA (Angle – Side – Angle) Congruence Rule: Two triangles are congruent, if two angles and the included side of one triangle are equal to two angles and the included side of the other triangle.
    • SAS (Side – Angle – Side) Congruence Rule: Two triangles are congruent, if two sides and the included angle of one triangle are equal to two sides and the included angle of the other triangle.
  • Properties of a Triangle
    1. Angle opposite to equal sides of an isosceles triangle are equal.
    2. The sides opposite to equal angles of a triangle are equal.
    3. If two sides of a triangle are unequal then the angle opposite to the longer side is larger.
    4. In any triangle, the side opposite to the larger angle is larger.
    5. The sum of any two sides of a triangle is greater than the third side.
    6. The difference between any two sides of a triangle is less than its third side.
    7. If the bisector of the vertical angle of a triangle bisects the base, then triangle is an isosceles triangle.
    8. The sum of any two sides of a triangle is greater than twice the median drawn to the third side.

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दर्शाइए कि समकोण त्रिभुज में कर्ण सबसे लंबी भुजा होती है।

ΔABC में, ∠B = 90° [∵ दिया है] इसलिए, ∠A < 90° और ∠C < 90° [∵∠A + ∠C = 90°] अतः, ΔABC में, ∠B > ∠C [∵∠B = 90° और ∠C < 90°] AC > AB … (1)
[∵ किसी त्रिभुज में, बड़े कोण की सम्मुख भुजा बड़ी होती है] इसीप्रकार, ΔABC में, ∠B > ∠A
[∵∠B = 90° और ∠A < 90°] AC > BC … (2)
[∵ किसी त्रिभुज में, बड़े कोण की सम्मुख भुजा बड़ी होती है]

समीकरण (1) और (2) से
AC > AB और AC > BC
अतः, कर्ण AC सबसे लंबी भुजा है।

In a triangle locate a point in its interior which is equidistant from all the sides of the triangle.

Draw the bisectors of ∠A, ∠B and ∠C, which intersect each other at O. Point O is equidistant from the three sides of ΔABC i.e.

OP = OQ = OR.

AD is an altitude of an isosceles triangle ABC in which AB = AC. Show that AD bisects BC.

In ΔABD and ΔACD,
∠ADB = ∠ADC [∵ Each 90°] AB = AC [∵ Given] AD = AD [∵ Common] Hence, ΔABD ≅ ΔACD [∵RHS Congruency Rule] BD = DC [∵ CPCT] Hence, AD bisects BC

ABC एक समकोण त्रिभुज है, जिसमें ∠A = 90° और AB = AC है। ∠B और ∠C ज्ञात कीजिए।

ΔABC में,
AB = AC [∵ दिया है] ∠B = ∠C [∵ समद्विभाहु त्रिभुज की बराबर भुजाओं के सम्मुख कोण बराबर होते हैं] ΔABC में,
∠A + ∠B + ∠C = 180°
⇒ 90° + ∠B + ∠C = 180° [∵∠A=90°] ⇒ 90°+∠B + ∠B = 180° [∵∠C = ∠B] ⇒ 2∠B = 180°-90° = 90°
⇒ ∠B = (90°)/2 = 45°
अतः, ∠B = ∠C = 90°

दर्शाइए कि किसी समबाहु त्रिभुज का प्रत्येक कोण 60° होता है।

ΔABC में,
AB = AC [∵ दिया है] ∠C = ∠B … (1)
[∵ समद्विभाहु त्रिभुज की बराबर भुजाओं के सम्मुख कोण बराबर होते हैं]

इसी प्रकार
ΔABC में,
AB = BC [∵ दिया है] ∠C = ∠A … (2)
[∵ समद्विभाहु त्रिभुज की बराबर भुजाओं के सम्मुख कोण बराबर होते हैं]

समीकरण (1) और (2) से
∠A = ∠B = ∠C … (3)

ΔABC में,
∠A + ∠B + ∠C = 180°
⇒∠A + ∠A + ∠A = 180° [∵ समीकरण (3) से] ⇒ 3∠A = 180°
⇒ ∠A = (180°)/3 = 60°
अतः, ∠A = ∠B = ∠C = 60°

ABC is an isosceles triangle with AB = AC. Draw AP ⊥ BC to show that ∠B = ∠C.

In ΔABP and ΔACP,
∠APB = ∠APC [∵ Each 90°] AB = AC [∵ Given] AP = AP [∵ Common] Hence, ΔABP ≅ ΔACP [∵RHS Congruency Rule] ∠B = ∠C [∵ CPCT]

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