M is a point on side BC of a triangle ABC such that AM is the bisector of BAC. Is it true to say that perimeter of the triangle is greater than 2AM ? Give reason for your answer.

Name: M is a point on side BC of a triangle ABC such that AM is the bisector of angle BAC. Is it true to say that perimeter of the triangle is greater than 2AM ? Give reason for your answer.
Uploaded: Wed, 2021-01-06 17:58
Description: M is a point on side BC of a triangle ABC such that AM is the bisector of angle BAC. Is it true to say that perimeter of the triangle is greater than 2AM ? Give reason for your answer.

M is a point on side BC of a triangle ABC such that AM is the bisector of angle BAC. Is it true to say that perimeter of the triangle is greater than 2AM ? Give reason for your answer.

#Exemplar Maths for Class 9
#Maths
#Triangles
#NCERT

#1.3
#7.2
#7.3
#7.4
#7.1
#9.1

1.0
1.0
1.0
1.0
2.0
2.0
2.0
3.0
3.0
3.0
4.0
4.0
4.0
4.0
5.0
5.0
5.0
5.0
5.0
6.0
6.0
6.0
7.0
7.0
7.0
7.0
8.0
8.0
8.0
8.0
9.0
9.0
9.0
10.0
10.0
10.0
10.0
11.0
11.0
11.0
12.0
12.0
13.0
14.0
15.0
16.0
17.0
18.0
19.0
20.0
21.0

M is a point on side BC of a triangle ABC such that AM is the bisector of $\angle$ BAC. Is it true to say that perimeter of the triangle is greater than 2AM ? Give reason for your answer.

Answers (1)

True

Solution.

Perimeter of $\triangle$ ABC = AB + BC + AC

In $\triangle$ AMB and $\triangle$ AMC

We know that sum of two sides of a triangle is greater than third side.

AB + BM > AM ......(1)

and AC + MC > AM ......(2)

By adding (1) and (2) equation

AB + BM + MC + AC > 2AM

Since, BC = BM + MC

$\therefore$ AB + BC + AC > 2AM

=> Perimeter of $\triangle$ ABC > 2AM

Hence the given statement is true.

Posted by

infoexpert24

View full answer

Exams

Colleges

Predictors

Resources

Quick links

Quick Links

Exams

Colleges

Resources

Colleges

Resources

Exams

Exams

Colleges

Resources

Diploma Colleges

Other Exams

Exams

Resources

Upcoming Events

Exams

Top Schools

Products & Resources

NCERT Study Material

Top Countries

Student Visas

Exams

Colleges

Exams

Colleges

Upcoming Events

Resources

Exams

Colleges & Courses

Predictors

Resources

Online Courses

Products

Engineering Preparation

Medical Preparation

Top Streams

Specializations

Resources

Top Providers

Exams

Colleges

Predictors

Resources

Resources

Exams

Colleges

Predictors & E-Books

Exams

Predictors & Articles

Colleges

Resources

Exams

Colleges

Resources

Top Courses & Careers

Colleges

Exams

Resources

Get Answers to all your Questions

M is a point on side BC of a triangle ABC such that AM is the bisector of BAC. Is it true to say that perimeter of the triangle is greater than 2AM ? Give reason for your answer.

Answers (1)

Posted by

infoexpert24

Similar Questions

Latest Question

Ask your Query

Welcome Back :)

Register to post Answer

Welcome Back :)

M is a point on side BC of a triangle ABC such that AM is the bisector of $\angle$ BAC. Is it true to say that perimeter of the triangle is greater than 2AM ? Give reason for your answer.