AD is a median of the triangle ABC. Is it true that AB + BC + CA > 2 AD? Give reason for your answer.

Solution:

It is given that

In triangle ABC, AD is the median

We know that

Sum of any two sides of a triangle is greater than the third side

AB + BD > AD …. (1)

AC + DC > AD ….. (2)

It can be written as

AB + (BD + DC) + AC > 2AD

So we get

AB + BC + AC > 2AD

Therefore, AB + BC + CA > 2 AD is true.

✦ Try This: PS is a median of the triangle PQR. Is it true that PQ + QR + RP > 2 PS? Give reason for your answer.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 7

NCERT Exemplar Class 9 Maths Exercise 7.2 Problem 9

AD is a median of the triangle ABC. Is it true that AB + BC + CA > 2 AD? Give reason for your answer

Summary:

The statement “AD is a median of the triangle ABC. Is it true that AB + BC + CA > 2 AD” is true

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