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 2 AM? Give reason for your answer.
Solution:
From the question
We know that
Sum of two sides of a triangle is greater than the third side
In ∆ ABM,
AB + BM > AM …. (1)
In ∆ ACM
AC + CM > AM …. (2)
Adding equation (1) and (2)
AB + BM + AC + CM > AM + AM
AB + AC + BC > 2AM
Therefore, it is true that the perimeter of the triangle is greater than 2 AM.
✦ Try This: M is a point on side QR of a triangle PQR such that PM is the bisector of ∠QPR. Is it true to say that perimeter of the triangle is greater than 2 PM? Give reason for your answer.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 7
NCERT Exemplar Class 9 Maths Exercise 7.2 Problem 10
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 2 AM? Give reason for your answer
Summary:
The statement “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 2 AM” is true
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