https://www.urbanpro.com/bangalore/gautam-pal # Gautam Pal

## Maths Teacher for classes 6th to 10th with 6 years experience and having my own YouTube Channel for clearing doubts

## Overview

## Languages Spoken

## Education

## Address

## Verified Info

## Teaches

## Reviews (4)

## FAQs

## Lessons (1)

## Answers by Gautam (24)

## Teaches

## Answers by Gautam Pal (24)

Yes. Urban Pro just matches and finds students for you based on your expertise. You have to convert them after talking to the students. Answered on 11/08/2019 Learn CBSE/Class 9/Mathematics/Unit 4-Geometry/Triangles/NCERT Solutions/Exercise 7.1

## Lessons (1)

Solving Inequalities

Bellandur, Bangalore, India - 560103.

23

Referral Discount: Get ₹ 500 off when you make a payment to start classes. Get started by Booking a Demo.

Details verified of Gautam Pal✕

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Education

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Maths Academy, is a Maths centric institute formed in 2013 when a batch of seven students with complaints of nervousness and poor track record passed out with marks in the range of 65%- 72%. It is formed with the sole intention to get satisfaction out of success stories of such students who have uneasiness with Maths.

Our teaching is styled to help everyone secure extra confidence through fast solving tricks, solving a particular question in as many different ways as possible, out-of-textbook method of guessing and approximation for Olympiads and entrance examinations, along with practical understanding of terminologies with their everyday application.

It is founded by me, Gautam Pal. A full time MBA from IMT Ghaziabad batch of 2010 and a B.E from NIT Durgapur of 2005, I have worked in IT and Manufacturing sector when the drive to do something for the younger generation inspired me to start my teaching journey. In a space of one year, I interacted with students across various boards and found out that Maths if taught with fun, practical insight, logical methodology and patience can be appreciated by all minds - rich or weak.

At Hello Maths Academy, we take academic courses of class V to X across various boards such as CBSE, ICSE, IB and State Board. Every child is taught his/her current year syllabus in addition to the earlier class content as revision. A bit of next year syllabus is also covered for topics that are going to be there for next year.

Our teaching is styled to help everyone secure extra confidence through fast solving tricks, solving a particular question in as many different ways as possible, out-of-textbook method of guessing and approximation for Olympiads and entrance examinations, along with practical understanding of terminologies with their everyday application.

It is founded by me, Gautam Pal. A full time MBA from IMT Ghaziabad batch of 2010 and a B.E from NIT Durgapur of 2005, I have worked in IT and Manufacturing sector when the drive to do something for the younger generation inspired me to start my teaching journey. In a space of one year, I interacted with students across various boards and found out that Maths if taught with fun, practical insight, logical methodology and patience can be appreciated by all minds - rich or weak.

At Hello Maths Academy, we take academic courses of class V to X across various boards such as CBSE, ICSE, IB and State Board. Every child is taught his/her current year syllabus in addition to the earlier class content as revision. A bit of next year syllabus is also covered for topics that are going to be there for next year.

Intro Video

- Class 9 Tuition , Class 10 Tuition +5

Bengali Mother Tongue (Native)

English Proficient

Marathi Proficient

Hindi Proficient

NIT Durgapur 2005

Bachelor of Engineering (B.E.)

IMT Ghaziabad 2010

Master of Business Administration (M.B.A.)

Bellandur, Bangalore, India - 560103

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Class 10 Tuition

Class Location

Online (video chat via skype, google hangout etc)

Student's Home

Tutor's Home

Years of Experience in Class 10 Tuition

7

Board

State, ICSE, CBSE, International Baccalaureate, IGCSE

State boards taught

Karnataka State Board

IB Subjects taught

Mathematics

Preferred class strength

Group Classes, One on one/ Private Tutions

CBSE Subjects taught

Mathematics

ICSE Subjects taught

Mathematics

IGCSE Subjects taught

Mathematics

Taught in School or College

No

State Syllabus Subjects taught

Mathematics

Teaching Experience in detail in Class 10 Tuition

Teaching Class X Mathematics is a process where a child is expected to have his fundamentals on arithmetic, algebra and geometry pretty robust. It is like constructing a building on a sound foundation. So my method involved around the why and how of Mathematics at this point. I stress upon the why and how so that a child doesn't have to be dependent on memorizing the formulas blindly without understanding the logic behind it. Continuous practice is the next approach to finetune his preparation for the final exam.

Class 6 Tuition

Class Location

Online (video chat via skype, google hangout etc)

Student's Home

Tutor's Home

Years of Experience in Class 6 Tuition

6

Board

ICSE, CBSE, IGCSE, International Baccalaureate, State

State boards taught

Karnataka State Board

IB Subjects taught

Mathematics

CBSE Subjects taught

Mathematics

ICSE Subjects taught

Mathematics

IGCSE Subjects taught

Mathematics

Taught in School or College

No

State Syllabus Subjects taught

Mathematics

Teaching Experience in detail in Class 6 Tuition

In Class 6 children are exposed to ideas which are to be continued for further 2 years and also to ideas which are to be the foundation basis for higher concepts in future. So I try to solve them a Maths question in as many different ways as possible so that they realize the inter-connectivity between different ideas and also realize that a Maths concept can be tackled by various methods but give them the freedom to solve the question as per the method they like. Also, giving real life examples is necessary so that they don't feel that Maths is a abstract subject.

Class 7 Tuition

Class Location

Online (video chat via skype, google hangout etc)

Student's Home

Tutor's Home

Years of Experience in Class 7 Tuition

6

Board

ICSE, CBSE, IGCSE, International Baccalaureate, State

State boards taught

Karnataka State Board

IB Subjects taught

Mathematics

CBSE Subjects taught

Mathematics

ICSE Subjects taught

Mathematics

IGCSE Subjects taught

Mathematics

Taught in School or College

No

State Syllabus Subjects taught

Mathematics

Teaching Experience in detail in Class 7 Tuition

In Class 7 children are mature enough to be exposed to basic questions and Olympiad questions. So after telling them the basic idea of a concept I give them Olympiad level questions so that they try to put their efforts into applying the basic ideas in solving the tough questions. Most of the time they are not successful, but that is where I tell them that I was also like them and only became better by understanding the problem and the method to solve it. So encouragement is very vital at this stage. Also, I try to solve them a Maths question in as many different ways as possible so that they realize the inter-connectivity between different ideas and also realize that a Maths concept can be tackled by various methods but give them the freedom to solve the question as per the method they like.

Class 8 Tuition

Class Location

Online (video chat via skype, google hangout etc)

Student's Home

Tutor's Home

Years of Experience in Class 8 Tuition

7

Board

ICSE, CBSE, IGCSE, International Baccalaureate, State

State boards taught

Karnataka State Board

IB Subjects taught

Mathematics

Preferred class strength

One on one/ Private Tutions

CBSE Subjects taught

Mathematics

ICSE Subjects taught

Mathematics

IGCSE Subjects taught

Mathematics

Taught in School or College

No

State Syllabus Subjects taught

Mathematics

Teaching Experience in detail in Class 8 Tuition

In Class 8 children are mature to be exposed to advanced ideas and this is where I push them by introducing to tough problems. They might not be able to solve them but they have to be encouraged and told that even I had failed to solve them when I was given such questions when I was of their age. I also try to solve them a Maths question in as many different ways as possible so that they realize the inter-connectivity between different ideas and also realize that a Maths concept can be tackled by various methods but give them the freedom to solve the question as per the method they like. Also, giving real life examples is necessary so that they don't feel that Maths is a abstract subject.

Class 9 Tuition

Class Location

Online (video chat via skype, google hangout etc)

Student's Home

Tutor's Home

Years of Experience in Class 9 Tuition

7

Board

State, ICSE, CBSE, International Baccalaureate, IGCSE

State boards taught

Karnataka State Board

IB Subjects taught

Mathematics

Preferred class strength

One on one/ Private Tutions

CBSE Subjects taught

Mathematics

ICSE Subjects taught

Mathematics, Technical Drawing Applications

IGCSE Subjects taught

Mathematics

Taught in School or College

No

State Syllabus Subjects taught

Mathematics

Teaching Experience in detail in Class 9 Tuition

Class 9 Mathematics is all about getting exposed to new concepts and applying all the concepts learnt in earlier classes, especially 6th, 7th and 8th. So a student has to be thorough with the basics and then he can be well geared to absorb newer learning taught in class 9th.

Class 11 Tuition

Class Location

Online (video chat via skype, google hangout etc)

Student's Home

Tutor's Home

Years of Experience in Class 11 Tuition

7

Board

CBSE, ISC/ICSE, IGCSE, State, International Baccalaureate

State boards taught

Karnataka State Board

IB Subjects taught

Mathematics

Preferred class strength

Group Classes, One on one/ Private Tutions

ISC/ICSE Subjects taught

Mathematics

CBSE Subjects taught

Mathematics

IGCSE Subjects taught

Mathematics

Taught in School or College

No

State Syllabus Subjects taught

Mathematics

Teaching Experience in detail in Class 11 Tuition

Class 11 requires extensive brush-up of previous concepts alongwith exhaustive practice of new learnt concepts. As a tutor, I try to remain self-motivated and keep asking students about whether they have understood everything or not.

Class 12 Tuition

Class Location

Online (video chat via skype, google hangout etc)

Student's Home

Tutor's Home

Years of Experience in Class 12 Tuition

7

Board

CBSE, ISC/ICSE, IGCSE, State, International Baccalaureate

IB Subjects taught

Mathematics

Preferred class strength

One on one/ Private Tutions

ISC/ICSE Subjects taught

Mathematics

CBSE Subjects taught

Mathematics

IGCSE Subjects taught

Mathematics

State board looking for

Karnataka State Board

Taught in School or College

No

State Syllabus Subjects taught

Mathematics

4 out of 5 4 reviews

Gautam Pal https://s3-ap-southeast-1.amazonaws.com/tv-prod/member/photo/598081-small.jpg Bellandur

4.0054 Gautam Pal

S

Swapnil

Reviewed on 10 Apr, 2020

"A sincere and hardworking tutor who is well equipped with concepts and take immense care to see that the child doesn't memorize the formula blindly but understands how and why it is. Good punctual and dedicated tutor. "

Gautam Pal

D

Debashis Pal

Reviewed on 07 Aug, 2019

"If you want a teacher to work as hard as your son or daughter, then Gautam Pal is the perfect choice. He understands a child and then prepares his own road map. He made my son understand arithmetic using different methods and solved questions from different textbooks and now he is confident with various arithmetic concepts. He is friendly and a passionate teacher who teaches from heart. "

Gautam Pal

H

Himadri

Reviewed on 04 Jul, 2019

"Conceptually very sound. Very good for students who are struggling with Maths. Always encourages a child to think and solve using the method which a student understands better. Friendly way of teaching. Have become my son's good friend. "

Gautam Pal

D

Deleted User

Reviewed on 22 Jun, 2019

"I would have rated him zero star, Gautam came to our house to take demo class and then he disagreed to continue the students because he got other students elsewhere, please be very careful in selecting him as a teacher for your kids. He leaves the just before exams without proper justification. "

Have you attended any class with Gautam? Write a Review

1. Which school boards of Class 10 do you teach for?

State, ICSE, CBSE and others

2. Do you have any prior teaching experience?

No

3. Which classes do you teach?

I teach Class 10 Tuition, Class 11 Tuition, Class 12 Tuition, Class 6 Tuition, Class 7 Tuition, Class 8 Tuition and Class 9 Tuition Classes.

4. Do you provide a demo class?

Yes, I provide a free demo class.

5. How many years of experience do you have?

I have been teaching for 7 years.

Solving Inequalities

In Mathematics, having a sound foundation/base is very essential to help us navigate through tough concepts in higher classes. Like, solving (x-4)^2 < 9; x>0. To solve...

Answered on 23/03/2022 Learn Tuition

Register yourself on urban Pro by creating a profile for the things you teach.

Like 0

Answers 77 Comments Answered on 23/03/2022 Learn Tuition

Yes. Urban Pro just matches and finds students for you based on your expertise. You have to convert them after talking to the students.

Like 0

Answers 72 Comments Answered on 11/08/2019 Learn CBSE/Class 9/Mathematics/Surface Area and Volumes/NCERT Solutions/Exercise 13.7

Diameter of the cone = 10.5m (Radius of the cone = 5.25m) Height of the cone = 3m Volume of the cone = (πr²h)/3 ∴ Volume of the cone = (π x 5.25² x 3)/3 = 86.625m³ The heap is to be covered by canvas to protect it from rain and we have to find the area of the canvas required.... ...more

Diameter of the cone = 10.5m (Radius of the cone = 5.25m)

Height of the cone = 3m

Volume of the cone = (πr²h)/3

∴ Volume of the cone = (π x 5.25² x 3)/3 = 86.625m³

The heap is to be covered by canvas to protect it from rain and we have to find the area of the canvas required. So, that means, we have to find the lateral surface area.

Lateral surface area of the cone = πr√r² + h²

∴ Lateral surface area of the cone = π x 5.25√5.25² + 3² = 99.77m²

∴ The area of the canvas required = 99.77m²

Like 0

Answers 4 Comments Answered on 11/08/2019 Learn CBSE/Class 9/Mathematics/Unit 4-Geometry/Triangles/NCERT Solutions/Exercise 7.1

(i) In ΔAMC and ΔBMD, AM = BM (M is the mid-point of hypotenuse AB) ∠AMC = ∠BMD (vertically opposite angles) CM = DM ΔAMC ≅ ΔBMD by SAS Test of congruency (ii) ∠ACM = ∠BDM (corressponding angles of congruent triangles) Also, ∠ACM and ∠BDM form... ...more

(i) In ΔAMC and ΔBMD,

AM = BM (M is the mid-point of hypotenuse AB)

∠AMC = ∠BMD (vertically opposite angles)

CM = DM

ΔAMC ≅ ΔBMD by SAS Test of congruency

(ii) ∠ACM = ∠BDM (corressponding angles of congruent triangles)

Also, ∠ACM and ∠BDM form alternate interior angles with CD as the transversal.

So, AC parallel to BD.

So, ∠ACB and ∠DBC form co-interior angle with BC as transversal.

So, ∠ACB + ∠DBC = 180° (co-interior angle adds up to 180°)

∠ACB = 90° (It is given that in triangle ABC, right angled at C)

So, ∠DBC = 90°. So, ∠DBC is a right angle.

(iii) ΔAMC ≅ ΔBMD by SAS Test of congruency

∴ AC = BD (corressponding sides of congruent triangles)

Now, in ΔDBC and ΔACB

BD = AC

∠DBC = ∠ACB (both are 90°)

BC = BC (common side)

∴ ΔDBC ≅ ΔACB by SAS Test of congruency

(iv) ∴ DC = AB (corressponding sides of congruent triangles)

∴ DM + MC = AB

∴ MC + MC = AB (It is given, DM = MC)

∴ 2 MC = AB

∴ MC = 1/2 AB

Like 0

Answers 1 Comments Answered on 11/08/2019 Learn CBSE/Class 9/Mathematics/Unit 4-Geometry/Triangles/NCERT Solutions/Exercise 7.1

In ΔABD and ΔBAC, AD = BC ∠DAB = ∠CBA AB = AB (common side) ∴ ΔABD ≅ ΔBAC by SAS Test of congruency ∴ BD = AC (corressponding sides of congruent traingles) ∴ ∠ABD = ∠BAC (corressponding angles of congruent traingles) ...more

In ΔABD and ΔBAC,

AD = BC

∠DAB = ∠CBA

AB = AB (common side)

∴ ΔABD ≅ ΔBAC by SAS Test of congruency

∴ BD = AC (corressponding sides of congruent traingles)

∴ ∠ABD = ∠BAC (corressponding angles of congruent traingles)

Like 0

Answers 1 Comments Class 10 Tuition

Class Location

Online (video chat via skype, google hangout etc)

Student's Home

Tutor's Home

Years of Experience in Class 10 Tuition

7

Board

State, ICSE, CBSE, International Baccalaureate, IGCSE

State boards taught

Karnataka State Board

IB Subjects taught

Mathematics

Preferred class strength

Group Classes, One on one/ Private Tutions

CBSE Subjects taught

Mathematics

ICSE Subjects taught

Mathematics

IGCSE Subjects taught

Mathematics

Taught in School or College

No

State Syllabus Subjects taught

Mathematics

Teaching Experience in detail in Class 10 Tuition

Teaching Class X Mathematics is a process where a child is expected to have his fundamentals on arithmetic, algebra and geometry pretty robust. It is like constructing a building on a sound foundation. So my method involved around the why and how of Mathematics at this point. I stress upon the why and how so that a child doesn't have to be dependent on memorizing the formulas blindly without understanding the logic behind it. Continuous practice is the next approach to finetune his preparation for the final exam.

Class 6 Tuition

Class Location

Online (video chat via skype, google hangout etc)

Student's Home

Tutor's Home

Years of Experience in Class 6 Tuition

6

Board

ICSE, CBSE, IGCSE, International Baccalaureate, State

State boards taught

Karnataka State Board

IB Subjects taught

Mathematics

CBSE Subjects taught

Mathematics

ICSE Subjects taught

Mathematics

IGCSE Subjects taught

Mathematics

Taught in School or College

No

State Syllabus Subjects taught

Mathematics

Teaching Experience in detail in Class 6 Tuition

In Class 6 children are exposed to ideas which are to be continued for further 2 years and also to ideas which are to be the foundation basis for higher concepts in future. So I try to solve them a Maths question in as many different ways as possible so that they realize the inter-connectivity between different ideas and also realize that a Maths concept can be tackled by various methods but give them the freedom to solve the question as per the method they like. Also, giving real life examples is necessary so that they don't feel that Maths is a abstract subject.

Class 7 Tuition

Class Location

Online (video chat via skype, google hangout etc)

Student's Home

Tutor's Home

Years of Experience in Class 7 Tuition

6

Board

ICSE, CBSE, IGCSE, International Baccalaureate, State

State boards taught

Karnataka State Board

IB Subjects taught

Mathematics

CBSE Subjects taught

Mathematics

ICSE Subjects taught

Mathematics

IGCSE Subjects taught

Mathematics

Taught in School or College

No

State Syllabus Subjects taught

Mathematics

Teaching Experience in detail in Class 7 Tuition

In Class 7 children are mature enough to be exposed to basic questions and Olympiad questions. So after telling them the basic idea of a concept I give them Olympiad level questions so that they try to put their efforts into applying the basic ideas in solving the tough questions. Most of the time they are not successful, but that is where I tell them that I was also like them and only became better by understanding the problem and the method to solve it. So encouragement is very vital at this stage. Also, I try to solve them a Maths question in as many different ways as possible so that they realize the inter-connectivity between different ideas and also realize that a Maths concept can be tackled by various methods but give them the freedom to solve the question as per the method they like.

Class 8 Tuition

Class Location

Online (video chat via skype, google hangout etc)

Student's Home

Tutor's Home

Years of Experience in Class 8 Tuition

7

Board

ICSE, CBSE, IGCSE, International Baccalaureate, State

State boards taught

Karnataka State Board

IB Subjects taught

Mathematics

Preferred class strength

One on one/ Private Tutions

CBSE Subjects taught

Mathematics

ICSE Subjects taught

Mathematics

IGCSE Subjects taught

Mathematics

Taught in School or College

No

State Syllabus Subjects taught

Mathematics

Teaching Experience in detail in Class 8 Tuition

In Class 8 children are mature to be exposed to advanced ideas and this is where I push them by introducing to tough problems. They might not be able to solve them but they have to be encouraged and told that even I had failed to solve them when I was given such questions when I was of their age. I also try to solve them a Maths question in as many different ways as possible so that they realize the inter-connectivity between different ideas and also realize that a Maths concept can be tackled by various methods but give them the freedom to solve the question as per the method they like. Also, giving real life examples is necessary so that they don't feel that Maths is a abstract subject.

Class 9 Tuition

Class Location

Online (video chat via skype, google hangout etc)

Student's Home

Tutor's Home

Years of Experience in Class 9 Tuition

7

Board

State, ICSE, CBSE, International Baccalaureate, IGCSE

State boards taught

Karnataka State Board

IB Subjects taught

Mathematics

Preferred class strength

One on one/ Private Tutions

CBSE Subjects taught

Mathematics

ICSE Subjects taught

Mathematics, Technical Drawing Applications

IGCSE Subjects taught

Mathematics

Taught in School or College

No

State Syllabus Subjects taught

Mathematics

Teaching Experience in detail in Class 9 Tuition

Class 9 Mathematics is all about getting exposed to new concepts and applying all the concepts learnt in earlier classes, especially 6th, 7th and 8th. So a student has to be thorough with the basics and then he can be well geared to absorb newer learning taught in class 9th.

Class 11 Tuition

Class Location

Online (video chat via skype, google hangout etc)

Student's Home

Tutor's Home

Years of Experience in Class 11 Tuition

7

Board

CBSE, ISC/ICSE, IGCSE, State, International Baccalaureate

State boards taught

Karnataka State Board

IB Subjects taught

Mathematics

Preferred class strength

Group Classes, One on one/ Private Tutions

ISC/ICSE Subjects taught

Mathematics

CBSE Subjects taught

Mathematics

IGCSE Subjects taught

Mathematics

Taught in School or College

No

State Syllabus Subjects taught

Mathematics

Teaching Experience in detail in Class 11 Tuition

Class 11 requires extensive brush-up of previous concepts alongwith exhaustive practice of new learnt concepts. As a tutor, I try to remain self-motivated and keep asking students about whether they have understood everything or not.

Class 12 Tuition

Class Location

Online (video chat via skype, google hangout etc)

Student's Home

Tutor's Home

Years of Experience in Class 12 Tuition

7

Board

CBSE, ISC/ICSE, IGCSE, State, International Baccalaureate

IB Subjects taught

Mathematics

Preferred class strength

One on one/ Private Tutions

ISC/ICSE Subjects taught

Mathematics

CBSE Subjects taught

Mathematics

IGCSE Subjects taught

Mathematics

State board looking for

Karnataka State Board

Taught in School or College

No

State Syllabus Subjects taught

Mathematics

4 out of 5 4 reviews

Gautam Pal

S

Swapnil

Reviewed on 10 Apr, 2020

"A sincere and hardworking tutor who is well equipped with concepts and take immense care to see that the child doesn't memorize the formula blindly but understands how and why it is. Good punctual and dedicated tutor. "

Gautam Pal

D

Debashis Pal

Reviewed on 07 Aug, 2019

"If you want a teacher to work as hard as your son or daughter, then Gautam Pal is the perfect choice. He understands a child and then prepares his own road map. He made my son understand arithmetic using different methods and solved questions from different textbooks and now he is confident with various arithmetic concepts. He is friendly and a passionate teacher who teaches from heart. "

Gautam Pal

H

Himadri

Reviewed on 04 Jul, 2019

"Conceptually very sound. Very good for students who are struggling with Maths. Always encourages a child to think and solve using the method which a student understands better. Friendly way of teaching. Have become my son's good friend. "

Gautam Pal

D

Deleted User

Reviewed on 22 Jun, 2019

"I would have rated him zero star, Gautam came to our house to take demo class and then he disagreed to continue the students because he got other students elsewhere, please be very careful in selecting him as a teacher for your kids. He leaves the just before exams without proper justification. "

Have you attended any class with Gautam? Write a Review

Answered on 23/03/2022 Learn Tuition

Register yourself on urban Pro by creating a profile for the things you teach.

Like 0

Answers 77 Comments Answered on 23/03/2022 Learn Tuition

Like 0

Answers 72 Comments Answered on 11/08/2019 Learn CBSE/Class 9/Mathematics/Surface Area and Volumes/NCERT Solutions/Exercise 13.7

Diameter of the cone = 10.5m (Radius of the cone = 5.25m) Height of the cone = 3m Volume of the cone = (πr²h)/3 ∴ Volume of the cone = (π x 5.25² x 3)/3 = 86.625m³ The heap is to be covered by canvas to protect it from rain and we have to find the area of the canvas required.... ...more

Diameter of the cone = 10.5m (Radius of the cone = 5.25m)

Height of the cone = 3m

Volume of the cone = (πr²h)/3

∴ Volume of the cone = (π x 5.25² x 3)/3 = 86.625m³

The heap is to be covered by canvas to protect it from rain and we have to find the area of the canvas required. So, that means, we have to find the lateral surface area.

Lateral surface area of the cone = πr√r² + h²

∴ Lateral surface area of the cone = π x 5.25√5.25² + 3² = 99.77m²

∴ The area of the canvas required = 99.77m²

Like 0

Answers 4 Comments Answered on 11/08/2019 Learn CBSE/Class 9/Mathematics/Unit 4-Geometry/Triangles/NCERT Solutions/Exercise 7.1

(i) In ΔAMC and ΔBMD, AM = BM (M is the mid-point of hypotenuse AB) ∠AMC = ∠BMD (vertically opposite angles) CM = DM ΔAMC ≅ ΔBMD by SAS Test of congruency (ii) ∠ACM = ∠BDM (corressponding angles of congruent triangles) Also, ∠ACM and ∠BDM form... ...more

(i) In ΔAMC and ΔBMD,

AM = BM (M is the mid-point of hypotenuse AB)

∠AMC = ∠BMD (vertically opposite angles)

CM = DM

ΔAMC ≅ ΔBMD by SAS Test of congruency

(ii) ∠ACM = ∠BDM (corressponding angles of congruent triangles)

Also, ∠ACM and ∠BDM form alternate interior angles with CD as the transversal.

So, AC parallel to BD.

So, ∠ACB and ∠DBC form co-interior angle with BC as transversal.

So, ∠ACB + ∠DBC = 180° (co-interior angle adds up to 180°)

∠ACB = 90° (It is given that in triangle ABC, right angled at C)

So, ∠DBC = 90°. So, ∠DBC is a right angle.

(iii) ΔAMC ≅ ΔBMD by SAS Test of congruency

∴ AC = BD (corressponding sides of congruent triangles)

Now, in ΔDBC and ΔACB

BD = AC

∠DBC = ∠ACB (both are 90°)

BC = BC (common side)

∴ ΔDBC ≅ ΔACB by SAS Test of congruency

(iv) ∴ DC = AB (corressponding sides of congruent triangles)

∴ DM + MC = AB

∴ MC + MC = AB (It is given, DM = MC)

∴ 2 MC = AB

∴ MC = 1/2 AB

Like 0

Answers 1 Comments

In ΔABD and ΔBAC, AD = BC ∠DAB = ∠CBA AB = AB (common side) ∴ ΔABD ≅ ΔBAC by SAS Test of congruency ∴ BD = AC (corressponding sides of congruent traingles) ∴ ∠ABD = ∠BAC (corressponding angles of congruent traingles) ...more

In ΔABD and ΔBAC,

AD = BC

∠DAB = ∠CBA

AB = AB (common side)

∴ ΔABD ≅ ΔBAC by SAS Test of congruency

∴ BD = AC (corressponding sides of congruent traingles)

∴ ∠ABD = ∠BAC (corressponding angles of congruent traingles)

Like 0

Answers 1 Comments Load More

In Mathematics, having a sound foundation/base is very essential to help us navigate through tough concepts in higher classes. Like, solving (x-4)^2 < 9; x>0. To solve...

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