NCERT Solutions Class 9 Exercise 7.4 of chapter 7-Triangles - Future Study Point

NCERT Solutions Class 9 Exercise 7.4 of chapter 7-Triangles

class 9 maths ex 7.4

NCERT Solutions Class 9 Exercise 7.4 of chapter 7-Triangles

NCERT Solutions of Class 9 Exercise 7.4 of chapter 7-Triangles are created here for helping the students of class 9 in helping their preparations for CBSE board exams. All NCERT Solutions of Class 9 Exercise 7.4 of chapter 7-Triangles are solved by an expert of maths in such a way that every student can understand easily without the help of anybody.

Click for online shopping

Future Study Point.Deal: Cloths, Laptops, Computers, Mobiles, Shoes etc

class 9 maths ex 7.4

You can download the pdf of NCERT solutions of chapter 7

pdf of class 9 NCERT solutions of the chapter 7 -Triangle

Exercise 7.1- Triangles

Exercise 7.2- Triangle

Exercise 7.4 – Triangle

Q1.Show that in a right-angled triangle, the hypotenuse is the longest triangle.

Ans.

ex.7.3 Q1 class 9 maths

 

GIVEN: ฮ”ABC is a right triangle,let โˆ B =90ยฐ

TO PROVE: Hypotenuse is the largest side in a right triangle

PROOF: โˆ B = 90ยฐ(given)

โˆ A + โˆ B + โˆ Cย  = 180ยฐ (angle sum property of the triangle)

โˆ A + 90ยฐ + โˆ Cย  = 180ยฐ

โˆ A + โˆ Cย  = 180ยฐ-90ยฐ= 90ยฐ

โˆ A and โˆ C must be acute angle

โˆดโˆ A < 90ยฐ and โˆ C < 90ยฐ

Therefore โˆ B is the largest angle

So, โˆ B >โˆ Aย  and โˆ B>โˆ C

AC> BC and AC > AB (in a triangle side opposite to larger angle is longer)

Hence AC(hypotenuse)ย  is the largest side in a right triangle

Q2.In the given figure sides AB and AC of ฮ”ABC are extended to points P and Q respectively .Also โˆ PBC < โˆ QCB. Show that AC > AB.

Q2 ex.7.3 class 9 maths

 

Ans.

GIVEN: In the fig. โˆ PBC < โˆ QCB

TO PROVE:AC > AB

PROOF: โˆ PBC < โˆ QCB(given)

โˆ ABC + โˆ PBC = 180ยฐ(linear pair)

โˆ PBC = 180ยฐ – โˆ ABC ….(i)

โˆ ACB + โˆ QCB = 180ยฐ(linear pair)

โˆ QCB = 180ยฐ – โˆ ACB ….(ii)

From equation (i) and equation (ii)

180ยฐ – โˆ ABC < 180ยฐ – โˆ ACB

โˆ ABC >โˆ  ACB

AC > AB (side opposite to larger angle is greater)

Q3.In the given figure , โˆ B < โˆ A, and โˆ C < โˆ D. Show that AD < BC.

Q3 ex.7.3 class 9 maths

 

Ans.

GIVEN: โˆ B < โˆ A, and โˆ C < โˆ D

TO PROVE:AD < BC

PROOF: โˆ B < โˆ A (given)

OA < OB….(i) (side opposite to larger angle is grater)

โˆ C < โˆ D

OD < OC…(ii) (side opposite to larger angle is grater)

From equation (i) and equation (ii)

OA + OD < OB + OC

AD < BC (from figure), Hence proved

Q4.AB and CD are respectively smallest and the longest side of quadrilateral ABCD(see the given figure). Show that โˆ A > โˆ C and โˆ B > โˆ D.

ex.7.3 Q4 class 9 maths

 

Ans.

GIVEN: AB and CD are respectively smallest and the longest side of quadrilateral ABCD

COSTRUCTION: Joining A to C and B to D

TO PROVE: (i) โˆ A > โˆ Cย  (ii)ย  โˆ B > โˆ D.

(i) PROOF: In ฮ”ABC

BC> AB (AB is the smallest side in ABCD)

โˆ BAC > โˆ ACB ….(i) (side opposite to larger angle is grater)

Inย ฮ”ADC

CD > AD (CD is the largest side in ABCD)

โˆ DAC > โˆ ACD….(ii)

Adding equation (i) and (ii)

โˆ BAC + โˆ DAC > โˆ ACB + โˆ ACD

โˆ A > โˆ C, Hence proved

PROOF: (ii)ย  โˆ B > โˆ D

In ฮ”ABD

AD> AB (AB is the smallest side in ABCD)

โˆ ABD > โˆ ADB ….(i) (side opposite to larger angle is grater)

In ฮ”ADC

CD > BC (CD is the largest side in ABCD)

โˆ DBC > โˆ BDC….(ii)

Adding equation (i) and (ii)

โˆ ABD +โˆ DBC > โˆ ADB + โˆ BDC

โˆ B > โˆ D, Hence proved

Q5.In the given figure , PR > PQ and PS bisects โˆ QPR , prove that โˆ PSR > PSQ.

ex.7.3 Q5 class 9 maths

 

Ans.

GIVEN:PR > PQ

PS bisects โˆ QPR

โˆ QPS = โˆ SPR

TO PROVE: โˆ PSR >โˆ  PSQ

PROOF: PR > PQ (given)

โˆ Q > โˆ R (side opposite to larger angle is grater)

In ฮ”PQS

โˆ Q + โˆ QPS + โˆ  PSQ = 180ยฐ(angle sum property of the triangle)

โˆ Q = 180ยฐ -(โˆ QPS + โˆ  PSQ)…..(i)

In ฮ”PSR

โˆ R + โˆ SPR + โˆ  PSR = 180ยฐ(angle sum property of the triangle)

โˆ R = 180ยฐ -(โˆ SPR + โˆ  PSR)…..(ii)

From (i) and (ii)

180ยฐ -(โˆ QPS + โˆ  PSQ) > 180ยฐ -(โˆ SPR + โˆ  PSR)

โˆ SPR + โˆ  PSR >โˆ QPS + โˆ  PSQ

Since PS bisects โˆ P, โˆ QPS = โˆ SPR

โˆ SPR + โˆ  PSR >โˆ SPR + โˆ  PSQ

โˆ  PSR >โˆ  PSQ, Hence proved

Q6. Show that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.

class 9 maths ex 7.3 Q6

Ans. Let A is an external point out of the line and ACโŠฅ BC

Let BC is a line and AB is a line segment drawn from the point A on the line BC

In triangle ฮ”ABC

โˆ B <โˆ C (since โˆ B is acute angle and โˆ C =90ยฐ)

AC < AB (side opposite to larger angle is grater)

Similarly all line segments drawn from A on the line BC are larger than AC

Therefore AC is the shortest side drawn from A on BC, Hence proved

You can compensate us by donating any amount of money for our survival

Our Paytm NO 9891436286

You can compensate us

Paytm number 9891436286

The money collected by us will be used for the education of poor students who leaves their study because of a lack of money.

NCERT Solutions of Science and Maths for Class 9,10,11 and 12

NCERT Solutions for class 9 maths

Chapter 1- Number SystemChapter 9-Areas of parallelogram and triangles
Chapter 2-PolynomialChapter 10-Circles
Chapter 3- Coordinate GeometryChapter 11-Construction
Chapter 4- Linear equations in two variablesChapter 12-Heron’s Formula
Chapter 5- Introduction to Euclid’s GeometryChapter 13-Surface Areas and Volumes
Chapter 6-Lines and AnglesChapter 14-Statistics
Chapter 7-TrianglesChapter 15-Probability
Chapter 8- Quadrilateral

NCERT Solutions for class 9 scienceย 

Chapter 1-Matter in our surroundingsChapter 9- Force and laws of motion
Chapter 2-Is matter around us pure?Chapter 10- Gravitation
Chapter3- Atoms and MoleculesChapter 11- Work and Energy
Chapter 4-Structure of the AtomChapter 12- Sound
Chapter 5-Fundamental unit of lifeChapter 13-Why do we fall ill ?
Chapter 6- TissuesChapter 14- Natural Resources
Chapter 7- Diversity in living organismChapter 15-Improvement in food resources
Chapter 8- MotionLast years question papers & sample papers

NCERT Solutions for class 10 maths

Chapter 1-Real numberChapter 9-Some application of Trigonometry
Chapter 2-PolynomialChapter 10-Circles
Chapter 3-Linear equationsChapter 11- Construction
Chapter 4- Quadratic equationsChapter 12-Area related to circle
Chapter 5-Arithmetic ProgressionChapter 13-Surface areas and Volume
Chapter 6-TriangleChapter 14-Statistics
Chapter 7- Co-ordinate geometryChapter 15-Probability
Chapter 8-Trigonometry

CBSE Class 10-Question paper of maths 2021 with solutions

CBSE Class 10-Half yearly question paper of maths 2020 with solutions

CBSE Class 10 -Question paper of maths 2020 with solutions

CBSE Class 10-Question paper of maths 2019 with solutions

NCERT Solutions for Class 10 Science

Chapter 1- Chemical reactions and equationsChapter 9- Heredity and Evolution
Chapter 2- Acid, Base and SaltChapter 10- Light reflection and refraction
Chapter 3- Metals and Non-MetalsChapter 11- Human eye and colorful world
Chapter 4- Carbon and its CompoundsChapter 12- Electricity
Chapter 5-Periodic classification of elementsChapter 13-Magnetic effect of electric current
Chapter 6- Life ProcessChapter 14-Sources of Energy
Chapter 7-Control and CoordinationChapter 15-Environment
Chapter 8- How do organisms reproduce?Chapter 16-Management of Natural Resources

NCERT Solutions for class 11 maths

Chapter 1-SetsChapter 9-Sequences and Series
Chapter 2- Relations and functionsChapter 10- Straight Lines
Chapter 3- TrigonometryChapter 11-Conic Sections
Chapter 4-Principle of mathematical inductionChapter 12-Introduction to three Dimensional Geometry
Chapter 5-Complex numbersChapter 13- Limits and Derivatives
Chapter 6- Linear InequalitiesChapter 14-Mathematical Reasoning
Chapter 7- Permutations and CombinationsChapter 15- Statistics
Chapter 8- Binomial Theoremย Chapter 16- Probability

CBSE Class 11-Question paper of maths 2015

CBSE Class 11 – Second unit test of maths 2021 with solutions

NCERT solutions for class 12 maths

Chapter 1-Relations and FunctionsChapter 9-Differential Equations
Chapter 2-Inverse Trigonometric FunctionsChapter 10-Vector Algebra
Chapter 3-MatricesChapter 11 – Three Dimensional Geometry
Chapter 4-DeterminantsChapter 12-Linear Programming
Chapter 5- Continuity and DifferentiabilityChapter 13-Probability
Chapter 6- Application of DerivationCBSE Class 12- Question paper of maths 2021 with solutions
Chapter 7- Integrals
Chapter 8-Application of Integrals

Class 12 Solutions of Maths Latest Sample Paper Published by CBSE for 2021-22 Term 2

Class 12 Maths Important Questions-Application of Integrals

Class 12 Maths Important questions on Chapter 7 Integral with Solutions for term 2 CBSE Board 2021-22

Solutions of Class 12 Maths Question Paper of Preboard -2 Exam Term-2 CBSE Board 2021-22

Solutions of class 12ย  maths question paper 2021 preboard exam CBSE Solution

 

 

 

 

2 thoughts on “NCERT Solutions Class 9 Exercise 7.4 of chapter 7-Triangles”

  1. As I website possessor I believe the content matter here is rattling magnificent , appreciate it for your hard work. You should keep it up forever! Best of luck. Karel Mallory Thill

  2. Hi Dear, are you genuinely visiting this web site daily, if so then you will definitely get good knowledge.| Joanne Rodolph Landmeier

Comments are closed.

Scroll to Top